Algebra 1 G9

Line Graphs

Line graphs are used to display the change in a set of data over a period of time. Skills Handbook
A multiple-line graph shows change in more than one category of data over time.
You can use a line graph to look for trends and make predictions.

Example

The data in the table below show the number of households, in thousands, that
have cable TV and the number of households that subscribe to newspapers in a
certain city. Graph the data.

Households With Cable TV and Newspapers (thousands)

Year 1980 1990 1995 2000 2005

Cable TV 15.2 51.9 60.5 68.6 73.9

Newspapers 62.2 62.3 58.2 55.8 53.3

Since the data show changes over time for two sets of data, use a double line
graph. The horizontal scale displays years. The vertical axis shows the number of
households for each category.

Number of Households Households With Cable TV
(thousands) Cable TV and Newspapers Newspaper

85
75
65
55
45
35
25
15

1980 1990 2000 2010
Year

Notice that there is a break in the vertical axis. You can use a zigzag line to indicate a
break from 0 to 15 since there is no data less than 15 to graph.

Exercises

Graph the data in each table. 

1. Market Share (percent) 2. Percent of Schools With Internet Access
Year 1997 1999 2001 2003
Year 2004 2005 2006 2007 Elementary 75 94 99 100
Rap/Hip Hop 12.1 13.3 11.4 10.8 Secondary 89 98 100 100
Pop 10.0 8.1 7.1 10.7
SOURCE: National Center for Education Statistics
SOURCE: Recording Industry of America
Skills Handbook
i 811

Circle Graphs

Skills Handbook A circle graph is an efficient way to present certain types of data. The entire
circle represents all of the data. Each section of the circle represents a part of the
whole and can be labeled with the actual data or the data expressed as a fraction,
decimal, or percent. The angles at the center are central angles, and each angle is
proportional to the percent or fraction of the total.

Example Favorite Musical Instruments

Students at a high school were asked to pick their favorite instrument. Instrument Number of Students
The table at the right shows the number of students who chose each Bass 35
instrument. Draw a circle graph for the data. Drums 103
Piano 150
Step 1  Add to find the total number. Guitar 182
35 + 103 + 150 + 182 = 470

Step 2  For each central angle, set up a proportion to find the measure.
Use a calculator to solve each proportion.

35 = 36a0° 103 = b 150 = 36c0° 182 = d
470 470 360° 470 470 360°

a ≈ 27° b ≈ 79° c ≈ 115° d ≈ 139°

Step 3  Use a compass to draw a circle. Step 4  Label each sector. Favorite Musical Instruments
  Draw the approximate central
  angles using a protractor. Guitar
182 students
139°
Piano Drums Bass
115° 27° 150 103 35
79° students students
students

Exercises

1. a. Use the data in the table to draw a circle graph. Methods of Transportation

b. A pproximately what percent of students Transportation Method Walk Bicycle Bus Car
ride the bus? 432 81

c.  Approximately how many times more students Number of Students 252 135

walk than ride in a car?

2. Data Collection  Survey your class to find out how they get to school. Use the

data to draw a circle graph.

812

Stem-and-Leaf Plots all digits last Skills Handbook
to the left of digit
A stem-and-leaf plot is a display of data that uses the digits of the data values. To last digit
make a stem-and-leaf plot, separate each number into a stem and a leaf. A stem
and leaf for the number 2.39 is shown at the right. 2.3 9

You can use a stem-and-leaf plot to organize data. The data below describe the stem leaf
price for the same notebook at several stores.

Notebook Prices: $2.39 $2.47 $2.43 $2.21 $2.33 $2.28 $2.26

Use the first two 2.2 1 6 8 Use the corresponding last
digits for the “stems.” 2.3 3 9 digits for the “leaves.”
2.4 3 7 Arrange the numbers in order.

Key: 2.4 ͉ 3 means 2.43

You can use a back-to-back stem-and-leaf plot to display two related data sets. The
stems are between two vertical bars, and the leaves are on each side. Leaves are
in increasing order from the stems. In the back-to-back stem-and-leaf plot below,
3|4|1 represents a commute time of 43 min in Town A and a commute time of
41 min in Town B.

Daily Commute (min)

Town A Town B

6643 4 11457

986444 5 02224

5210 6 4589

876642 7 367999

Key: 7 ͉ 3 means 73
2 ͉ 7 means 72
2͉7͉3

Exercises

Make a stem-and-leaf plot for each set of data.

1. 18 35 28 15 36 10 25 22 15 2. 18.6 18.4 17.6 15.7 15.3 17.5

3. 785 776 788 761 768 768 785 4. 0.8 0.2 1.4 3.5 4.3 4.5 2.6 2.2

5. Make a back-to-back stem-and-leaf plot of the test scores
of the two classes below.
Class A: 98 78 85 72 94 81 68 83
Class B: 87 91 79 75 90 81 82 100

Skills Handbook i 813

Reference

Table 1  Measures

Reference United States Customary Metric
10 millimeters (mm) = 1 centimeter (cm)
Length 12 inches (in.) = 1 foot (ft)
36 in. = 1 yard (yd) 100 cm = 1 meter (m)
3 ft = 1 yard 1000 mm = 1 meter

5280 ft = 1 mile (mi) 1000 m = 1 kilometer (km)
1760 yd = 1 mile
100 square millimeters (mm2) = 1 square centimeter (cm2)
Area 144 square inches (in.2) = 1 square foot (ft2) 10,000 cm2 = 1 square meter (m2)
9 ft2 = 1 square yard (yd2) 10,000 m2 = 1 hectare (ha)

43,560 ft2 = 1 acre (a) 1000 cubic millimeters (mm3) = 1 cubic centimeter (cm3)
4840 yd2 = 1 acre 1,000,000 cm3 = 1 cubic meter (m3)

Volume 1728 cubic inches (in.3) = 1 cubic foot (ft3) 1000 milliliters (mL) = 1 liter (L)
27 ft3 = 1 cubic yard (yd3) 1000 L = 1 kiloliter (kL)

Liquid 8 fluid ounces (fl oz) = 1 cup (c) 1000 milligrams (mg) = 1 gram (g)
Capacity 2 c = 1 pint (pt) 1000 g = 1 kilogram (kg)
2 pt = 1 quart (qt) 1000 kg = 1 metric ton
4 qt = 1 gallon (gal) 0°C = freezing point of water
37°C = normal human body temperature
Weight 16 ounces (oz) = 1 pound (lb)
100°C = boiling point of water
or Mass 2000 pounds = 1 ton (t)



Temperature 32°F = freezing point of water
98.6°F = normal human body

temperature
212°F = boiling point of water

Customary Units and Metric Units

Length 1 in. = 2.54 cm
1 mi ≈ 1.61 km
1 ft ≈ 0.305 m

Capacity 1 qt ≈ 0.946 L

Weight 1 oz ≈ 28.4 g
and Mass 1 lb ≈ 0.454 kg

Time

60 seconds (s) = 1 minute (min) 4 weeks (approx.) = 1 month (mo) 12 months = 1 year

60 minutes = 1 hour (h) 365 days = 1 year (yr) 10 years = 1 decade

24 hours = 1 day (d) 52 weeks (approx.) = 1 year 100 years = 1 century

7 days = 1 week (wk)

814

Table 2  Reading Math Symbols

# Symbols Words Symbols Words

multiplication sign, times (×) ∠A angle A

= equals m∠A measure of angle A

≟ Are the statements equal? △ABC triangle ABC Reference

≈ is approximately equal to (x, y) ordered pair

∙ is not equal to x1, x2, . . . specific values of the

< is less than variable x

> is greater than y1, y2, . . . specific values of the

≤ is less than or equal to variable y

≥ is greater than or equal to x mean of data values of x

≅ is congruent to s standard deviation

{ plus or minus f(x) f of x; the function
( ) parentheses for grouping value at x

[ ] brackets for grouping m slope of a line

{ } set braces b y-intercept of a line

% percent a : b ratio of a to b

|a| absolute value of a 13 matrix
J2 4R
c and so on
- a opposite of a sin A sine of ∠A

p pi, an irrational number, cos A cosine of ∠A
approximately equal to 3.14
tan A tangent of ∠A

° degree(s) n! n factorial
an nth power of a
nPr p ermutations of n objects
2x nonnegative square arranged r at a time
root of x
nCr combinations of n objects
1 , a ∙ 0 reciprocal of a chosen r at a time
a
a<A–Bn> 1 P (event) probability of an event
an , a ∙ 0
^ raised to a power (in a
line through points A and B spreadsheet formula)

AB segment with endpoints * multiply (in a spreadsheet
formula)
A and B

AB length of AB; distance between / divide (in a spreadsheet
formula)
points A and B

Reference i 815

Properties and Formulas

Chapter 1 Foundations for Algebra Chapter 2 Solving Equations

Reference Order of Operations Addition Property of Equality
1. Perform an operation(s) inside grouping symbols.
2. Simplify powers. For every real number a, b, and c, if a = b, then
3. Multiply and divide from left to right. a + c = b + c.
4. Add and subtract from left to right.
Subtraction Property of Equality
Commutative Property of Addition
For every real number a, b, and c, if a = b, then
For every real number a and b, a + b = b + a. a - c = b - c.

# #Commutative Property of Multiplication # #Multiplication Property of Equality

For every real number a and b, a b = b a. For every real number a, b, and c, if a = b, then a c = b c.

Associative Property of Addition Division Property of Equality
For every real number a, b, and c, where c ≠ 0, if a = b,
For every real number a, b, and c, a b
(a + b) + c = a + (b + c). then c = c .

Associative Property of Multiplication Cross Products of a Proportion
a c
# # # #For every real number a, b, and c, If b = d , then ad = bc.

(a b) c = a (b c). Percent Proportion
a p
Identity Property of Addition b = 100 , where b ≠ 0.

For every real number a, a + 0 = a. #Percent Equation

#Identity Property of Multiplication a = p% b, where b ≠ 0.

For every real number a, 1 a = a. Simple Interest Formula

#Multiplication Property of − 1 I = prt

For every real number a, - 1 a = - a. Percent of Change

#Zero Property of Multiplication p% = amount of increase or decrease
original amount
For every real number a, a 0 = 0. amount of increase = new amount - original amount
amount of decrease = original amount - new amount
Inverse Property of Addition
Relative Error
For every real number a, there is an additive inverse 0 measured or estimated value - actual value 0
- a such that a + ( - a) = 0. relative error = actual value

Inverse Property of Multiplication
#For every nonzero number a, there is a multiplicative inverse
such that a 1 = 1. Chapter 3 Solving Inequalities
a
The following properties of inequality are also true for
Distributive Property Ú and … .
For every real number a, b, and c:
Addition Property of Inequality
a(b + c) = ab + ac
(b + c)a = ba + ca For every real number a, b, and c,
a(b - c) = ab - ac if a 7 b, then a + c 7 b + c;
(b - c)a = ba - ca if a 6 b, then a + c 6 b + c.

816

Subtraction Property of Inequality Chapter 5  Linear Functions

For every real number a, b, and c, Slope vertical change
if a 7 b, then a - c 7 b - c; horizontal change
if a 6 b, then a - c 6 b - c. slope = = rise
run

Multiplication Property of Inequality Direct Variation Reference

For every real number a, b, and c, where c 7 0, A direct variation is a relationship that can be represented by
if a 7 b, then ac 7 bc; a function of the form y = kx, where k ≠ 0.
if a 6 b, then ac 6 bc.
For every real number a, b, and c, where c 6 0, Slope-Intercept Form of a Linear Equation
if a 7 b, then ac 6 bc;
if a 6 b, then ac 7 bc. The slope-intercept form of a linear equation is

Division Property of Inequality y = mx + b, where m is the slope and b is the
y-intercept.

For every real number a, b, and c, where c 7 0, Point-Slope Form of a Linear Equation
a b
if a 7 b, then c 7 c ; The point-slope form of the equation of a nonvertical line
that passes through the point (x1, y1) with slope m is
if a 6 b, then a 6 b . y - y1 = m(x - x1).
c c
For every real number a, b, and c, where c 6 0, Standard Form of a Linear Equation
a b
if a 7 b, then c 6 c ; The standard form of a linear equation is Ax + By = C,
where A, B, and C are real numbers and A and B are not
if a 6 b, then a 7 b . both zero.
c c

Reflexive Property of Equality Slopes of Parallel Lines

For every real number a, a = a. Nonvertical lines are parallel if they have the same slope and

Symmetric Property of Equality different y-intercepts. Any two vertical lines are parallel.

For every real number a and b, Slopes of Perpendicular Lines
if a = b, then b = a.
Two lines are perpendicular if the product of their slopes is
Transitive Property of Equality
- 1. A vertical line and horizontal line are perpendicular.
For every real number a, b, and c,
if a = b and b = c, then a = c. Residual

Transitive Property of Inequality A residual is the difference between the y-value of a data
point and the corresponding y-value of a model for the data
For every real number a, b, and c, set. You can find a residual by calculating y - yˆ , where y
if a 6 b and b 6 c, then a 6 c. represents the y-value of the data set and y represents the
corresponding y-value predicted from the model.
Chapter 4  An Introduction to Functions
Chapter 6  Systems of Equations
Arithmetic Sequence
and Inequalities
The explicit form for the rule of an arithmetic sequence is
A(n) = A(1) + (n - 1)d, where A(n) is the nth term, Solutions of Systems of Linear Equations
A(1) is the first term, n is the term number, and
d is the common difference. A system of linear equations can have one solution, no
solution, or infinitely many solutions:
The recursive form for the rule of an arithmetic sequence is • If the lines have different slopes, the lines intersect, so
A(n) = A(n - 1) + d; A(1) = a, where A(n) is the nth term,
a is the first term, n is the term number, and d is the there is one solution.
common difference. • If the lines have the same slopes and different

y-intercepts, the lines are parallel, so there are no
solutions.
• If the lines have the same slopes and the same
y-intercepts, the lines are the same, so there are infinitely
many solutions.

Reference i 817

Chapter 7  Exponents and Chapter 8  Polynomials and Factoring

Exponential Functions Factoring Special Cases

Zero as an Exponent For every nonzero number a and b:
a2 - b2 = (a + b)(a - b)
For every nonzero number a, a0 = 1. a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2
a2 - 2ab + b2 = (a - b)(a - b) = (a - b)2
Negative Exponent
For every nonzero number a and rational number n,
Reference a-n 1
= an . Chapter 9  Quadratic Functions

Multiplying Powers With the Same Base and Equations
#For every nonzero number a and rational numbers m and n,
Graph of a Quadratic Function
am an = am + n.
The graph of y = ax2 + bx + c, where a ≠ 0, has the line
Dividing Powers With the Same Base xve=rte-x2abisa-2sabit.s axis of symmetry. The x-coordinate of the
For every nonzero number a and rational numbers m and n,
am - Zero-Product Property
an = am n.
For every real number a and b, if ab = 0, then
Raising a Power to a Power a = 0 or b = 0.
For every nonzero number a and rational numbers m and n,
(am)n = amn.

Raising a Product to a Power Quadratic Formula

For every nonzero number a and b and rational number n, If ax2 + bx + c = 0, where a ≠ 0, then
(ab)n = anbn. 2b2
x = -b { 2a - 4ac .

Raising a Quotient to a Power Property of the Discriminant
For every nonzero number a and b and rational number n,
( )a n an For the quadratic equation ax2 + bx + c = 0, where a ≠ 0,
b = bn . the value of the discriminant b2 - 4ac tells you the number
of solutions.
Properties of Rational Exponents
• If b2 - 4ac 7 0, there are two real solutions.
If the nth root of a is a real number and m is an integer, then • If b2 - 4ac = 0, there is one real solution.
1 2n a m 2n am 12n a2m. • If b2 - 4ac 6 0, there are no real solutions.
an = and an = = If m is negative,

a ≠ 0.

#Exponential Growth and Decay Chapter 10  Radical Expressions

An exponential function has the form y = a bx, where a is a and Equations
nonzero constant, b is greater than 0 and not equal to 1, and
The Pythagorean Theorem
#x is a real number.
In a right triangle, the sum of the squares of the lengths
• The function y = a bx , where b is the growth factor, of the legs is equal to the square of the length of the
hypotenuse: a2 + b2 = c2.
#models exponential growth for a 7 0 and b 7 1.
The Converse of the Pythagorean Theorem
• The function y = a bx , where b is the decay factor,
models exponential decay for a 7 0 and 0 6 b 6 1. If a triangle has sides of lengths a, b, and c, and
a2 + b2 = c2, then the triangle is a right triangle with
Geometric Sequence hypotenuse of length c.

#The explicit form for the rule of a geometric sequence is #Multiplication Property of Square Roots

A(n) = a r n - 1, where A(n) is the nth term, a is the first For every number a Ú 0 and b Ú 0, 2ab = 2a 2b.
term, n is the term number, and r is the common ratio.

#The recursive form for the rule of a geometric sequence is

A(n) = A(n – 1) r; A(1) = a, where A(n) is the nth term, a
is the first term, n is the term number, and r is the common
ratio.

818

Division Property of Square Roots Combination Notation

For every number a Ú 0 and b 7 0, a = 1a . The expression nCr represents the number of combinations
1b of n objects chosen r at a time.
5b

Trigonometric Ratios nCr = n! r)!
length of leg opposite ∠A r !(n -
sine of ∠A = length of hypotenuse
Theoretical Probability
length of leg adjacent to ∠A
cosine of ∠A = length of hypotenuse P(event) = number of favorable outcomes Reference
number of possible outcomes

tangent of ∠A = length of leg opposite ∠A Probability of an Event and Its Complement
length of leg adjacent to ∠A
P (event) + P (not event) = 1, or
Chapter 11  Rational Expressions P (not event) = 1 - P (event)

and Functions Odds

Inverse Variation Odds in favor of an event = number of favorable outcomes
number of unfavorable outcomes

An inverse variation is a relationship that can be represented Odds against an event = number of unfavorable outcomes
number of favorable outcomes
= k ≠
by a function of the form y x , where k 0. Experimental Probability

P(event) = number of times the event occurs
number of times the experiment is done
Chapter 12  Data Analysis and Probability
Probability of Mutually Exclusive Events
Mean
If A and B are mutually exclusive events, then
The mean of a set of data values = sum of the data values . P(A or B) = P(A) + P(B) .
total number of data values
Probability of Overlapping Events
Standard Deviation
If A and B are overlapping events, then
Standard deviation is a measure of how the values in a data P(A or B) = P(A) + P(B) - P(A and B) .

set vary, or deviate from the mean.

s = 5 Σ(x - x )2 Probability of Two Independent Events
n
#If A and B are independent events, then
Multiplication Counting Principle
P(A and B) = P(A) P(B) .
#If there are m ways to make a first selection and n ways to
Probability of Two Dependent Events
make a second selection, there are m n ways to make the
two selections. #If A and B are independent events, then

Permutation Notation P(A then B) = P(A) P(B after A) .

The expression nPr represents the number of permutations of
n objects arranged r at a time.
n!
nPr = (n - r)!

Reference i 819

Reference Formulas of  Geometry w s

You will use a number / P = 4s
of geometric formulas P = 2/ + 2w A = s2
as you work through your A = /w Square
algebra book. Here are Rectangle
some perimeter, area,
and volume formulas.

r h h
d
b
b A = bh
Parallelogram
C = 2pr or C = pd A = 1 bh
A = pr2 2

Circle Triangle

b1

h h

h

w base

b2 /
V = Bh
A = 1 (b1 + b2)h V = /wh V = 1 Bh
2 3
Right Prism
Trapezoid Pyramid

r

h base h
r
r
base
V = Bh
V = pr 2h V = 1 Bh V = 4 pr 3
Right Cylinder 3 3
1 pr 2h
V = 3

Right Cone Sphere

820

Visual Glossary

English Spanish

A Visual Glossary

Absolute value (p. 31)  The distance that a number is from Valor absoluto (p. 31)  La distancia a la que un número
zero on a number line. está del cero en una recta numérica.

Example -7 is 7 units from 0, so

0 -7 0 = 7.

Absolute value function (p. 346)  A function with a Función de valor absoluto (p. 346)  Función cuya gráfica
forma una V que se abre hacia arriba o hacia abajo. La
V-shaped graph that opens up or down. The parent function función madre de la familia de funciones de valor absoluto

for the family of absolute value functions is y = 0 x 0 . es y = 0 x 0 .

Example y x
2 24

O
Ϫ2

Additive inverse (p. 32)  The opposite or additive inverse Inverso aditivo (p. 32)  El opuesto o inverso aditivo de
of any number a is - a. The sum of opposites is 0. cualquier número a es -a. La suma de los opuestos es 0.

Example -5 and 5 are additive inverses
because -5 + 5 = 0.

Algebraic expression (p. 4)  A mathematical phrase that Expresión algebraica (p. 4)  Frase matemática que
includes one or more variables. contiene una o más variables.

Example 7 + x is an algebraic expression.

Angle of depression (p. 648)  An angle from the Ángulo de depresión (p. 648)  Un ángulo de la horizontal
horizontal down to a line of sight. It is used to measure hacia la línea de vista. Ángulo con que se miden
heights indirectly. indirectamente las alturas.

Example angle of depression horizontal

line of
sight

Glossary i 821

English Spanish

Visual Glossary Angle of elevation (p. 648)  An angle from the horizontal Ángulo de elevación (p. 648)  Ángulo de la horizontal
up to a line of sight. It is used to measure heights indirectly. hacia la línea de vista. Ángulo con que se miden las alturas
indirectamente.
Example

line of
sight

horizontal angle of elevation

Arithmetic sequence (p. 275)  A number sequence Progresión aritmética (p. 275)  En una progresión
formed by adding a fixed number to each previous term to aritmética la diferencia entre términos consecutivos es un
find the next term. The fixed number is called the common número constante. El número constante se llama la
difference. diferencia común.

Example 4, 7, 10, 13, c is an arithmetic
sequence.

Asymptote (p. 700)  A line that the graph of a function Asíntota (p. 700)  Línea recta a la que la gráfica de una
gets closer to as x or y gets larger in absolute value. función se acerca indefinidamente, mientras el valor
absoluto de x o y aumenta.

Example y

Ϫ2 1 2 x
O

Ϫ2

The y-axis is a vertical asymptote
for y = 1x. The x-axis is a
horizontal asymptote for y = 1x .

Axis of symmetry (p. 546)  The line that divides a Eje de simetría (p. 546)  El eje de simetría es la línea que
parabola into two matching halves. divide una parábola en dos mitades exactamente iguales.

Example 2y
x

O2
axis of
symmetry

822

English Spanish

B

Base (p. 10)  El número que se multiplica repetidas veces.
# # # #Base (p. 10)  A number that is multiplied repeatedly.
Example 45 = 4 4 4 4 4. The base Visual Glossary
4 is used as a factor 5 times.

Bias (p. 755)  A sampling error that causes one option to Parcialidad (p. 755)  Error de muestreo que hace que una
seem better than another. Survey questions or samples can opción parezca mejor que otra. Preguntas en una encuesta o
be biased. muestras pueden ser parciales.

Binomial (p. 487)  A polynomial of two terms. Binomio (p. 487)  Polinomio compuesto de dos términos.

Example 3x + 7 is a binomial.

Bivariate (p. 754)  A set of data that uses two variables is Bivariado (p. 754)  Un conjunto de datos que usa dos
bivariate. variables es bivariado.

Box-and-whisker plot (p. 747)  A graph that summarizes Gráfica de cajas (p. 747)  Gráfica que resume los datos a lo
data along a number line. The left whisker extends from the largo de una recta numérica. El brazo izquierdo se extiende
minimum to the first quartile. The box extends from the first desde el valor mínimo del primer cuartil. La caja se extiende
quartile to the third quartile and has a vertical line through desde el primer cuartil hasta el tercer cuartil y tiene una línea
the median. The right whisker extends from the third quartile vertical que atraviesa la mediana. El brazo derecho se
to the maximum. extiende desde el tercer cuartil hasta el valor máximo.

Example

12 345678

Q1 Q2 Q3

Box
Whiskers

C Causalidad (p. 340)  Cuando un cambio en una cantidad
causa un cambio en una segunda cantidad. Una correlación
Causation (p. 340)  When a change in one quantity causes entre las cantidades no implica siempre la causalidad.
a change in a second quantity. A correlation between
quantities does not always imply causation.

Coefficient (p. 48)  The numerical factor when a term has a Coeficiente (p. 48)  Factor numérico de un término que
variable. contiene una variable.

Example In the expression 2x + 3y + 16,
2 and 3 are coefficients.

Combination (p. 765)  Any unordered selection of r Combinación (p. 765)  Cualquier selección no ordenada

objects from a set of n objects is a combination. The number de r objetos tomados de un conjunto de n objetos es una

of combinations of n objects taken r at a time is combinación. El número de combinaciones de n objetos,
n! n!
nCr = r!(n - r)! for 0 … r … n. cuando se toman r objetos cada vez, es nCr = r!(n - r)! para
0…r… n.

Example The number of combinations of

seven items taken four at a time is
7!
7C4 = 4!(7 - 4)! = 35.

There are 35 ways to choose

four items from seven items

without regard to order.

Glossary i 823

English Spanish

Common difference (p. 275)  The difference between Diferencia común (p. 275)  La diferencia común es la
consecutive terms of an arithmetic sequence. diferencia entre los términos consecutivos de una progresión
aritmética.
Visual Glossary
Example The common difference is 3 in the
arithmetic sequence 4, 7, 10, 13, c

Common ratio (p. 467)  The fixed number used to find Razón común (p. 467)  Número constante que se usa para
terms in a geometric sequence. hallar los términos en una progresión geométrica.

Example The common ratio is 1 in
3
the geometric sequence
9, 3, 1, 13, c

Complement of an event (p. 770)  All possible outcomes Complemento de un suceso (p. 770)  Todos los

that are not in the event. resultados posibles que no se dan en el suceso.
P (complement of event) = 1 - P (event) P (complemento de un suceso) = 1 - P (suceso)

Example The complement of rolling a 1 or a 2 on a
number cube is rolling a 3, 4, 5, or 6.

Complement of a set (p. 196)  The set of all elements in Complemento de un conjunto (p. 196) 
the universal set that are not in a given set. Conjunto de todos los elementos en
el conjunto universal que no se incluyen en
el conjunto dado.

Example If U = 5 c , -3, -2, -1, 0, 1, 2, 3, c6
and A = 50, 1, 2, 3, c6, then the
complement of A is A′ = 5 c , -3, -2, -16.

Completing the square (p. 576)  A method of solving Completar el cuadrado (p. 576)  Método para solucionar
quadratic equations. Completing the square turns every ecuaciones cuadráticas. Cuando se completa el cuadrado, se
quadratic equation into the form x2 = c. transforma la ecuación cuadrática a la fórmula x2 = c.

Example x2 + 6x - 7 = 9 is rewritten as
(x + 3)2 = 25 by completing the
square.

Complex fraction (p. 528)  A fraction that has a fraction Fracción compleja (p. 528)  Una fracción compleja es una
in its numerator or denominator or in both its numerator fracción que contiene otra fracción en el numerador o en el
and denominator. denominador, o en ambos.

2
7
Example 3

2

Compound event (p. 776)  An event that consists of two Suceso compuesto (p. 776)  Suceso que consiste en dos o
or more events linked by the word and or the word or. más sucesos unidos por medio de la palabra y o la palabra o.

Example Rolling a 5 on a number cube
and then rolling a 4 is a
compound event.

824

English Spanish

Compound inequalities (p. 200)  Two inequalities that Desigualdades compuestas (p. 200)  Dos desigualdades
are joined by and or or. que están enlazadas por medio de una y o una o.

Examples 5 6 x and x 6 10 Visual Glossary
14 6 x or x … - 3

Compound interest (p. 461)  Interest paid on both the Interés compuesto (p. 461)  Interés calculado tanto sobre
principal and the interest that has already been paid. el capital como sobre los intereses ya pagados.

Example For an initial deposit of $1000 at a

6% interest rate with interest

compounded quarterly, the function

bya=la1n0ce00y1a0f.4t0e6r2xx gives the account
years.

Conclusion (p. 616)  The conclusion is the part of an Conclusión (p. 616) La conclusión es lo que sigue a la
if-then statement (conditional) that follows then. palabra entonces en un enunciado condicional.

Example In the conditional “If an animal
has four legs, then it is a horse,”
the conclusion is “it is a horse.”

Conditional (p. 616)  A conditional is an if-then statement. Condicional (p. 616) Un enunciado condicional es del tipo
si . . ., entonces . . .

Example If an animal has four legs, then it
is a horse.

Conditional probability (p. 783)  A probability that Probabilidad condicional (p. 783)  Probabilidad que
contains a condition that may limit the sample space for contiene una condición que puede limitar el espacio de
an event. The notation P(B | A) is read “the probability of muestra de un suceso. La notación P(B | A) se lee “la
event B, given event A.” probabilidad del suceso B, dado el suceso A.”

Conjugates (p. 627)  The sum and the difference of the Valores conjugados (p. 627)  La suma y resta de los
same two terms. mismos dos términos.

Example ( 13 + 2) and (13 - 2) are
conjugates.

Consistent system (p. 365)  A system of equations that Sistema consistente (p. 365)  Un sistema de ecuaciones
has at least one solution is consistent. que tiene por lo menos una solución es consistente.

Example y

Ϫ2 O 2x
Ϫ2

Glossary i 825

English Spanish

Constant (p. 48)  A term that has no variable factor. Constante (p. 48)  Término que tiene un valor fijo.

Visual Glossary Example In the expression 4x + 13y + 17,
17 is a constant term.

Constant of variation for direct variation (p. 301)  Constante de variación en variaciones directas
The nonzero constant k in the function y = kx. (p. 301)  La constante k cuyo valor no es cero en la
función y = kx.

Example For the direct variation y = 24x, 24 is
the constant of variation.

Constant of variation for inverse variation (p. 692)  Constante de variación en variaciones inversas
The nonzero constant k in the function y = kx. (p. 692)  La constante k cuyo valor no es cero en la
función y = kx.

Example For the inverse variation y = 8 ,
x
8 is the constant of variation.

Continuous graph (p. 255)  A graph that is unbroken. Gráfica continua (p. 255)  Una gráfica continua es una
Example gráfica ininterrumpida.

y
2

Ϫ2 O 2x
Ϫ2

Converse (p. 616)  The statement obtained by reversing the Expresión recíproca (p. 616)  Enunciado que se obtiene al
hypothesis and conclusion of a conditional. intercambiar la hipótesis y la conclusión de un enunciado
condicional.

Example The converse of “If I was born in
Houston, then I am a Texan” is
“If I am a Texan, then I was born
in Houston.”

Conversion factor (p. 117)  A ratio of two equivalent Factor de conversion (p. 117)  Razón de dos medidas
measures in different units. equivalentes en unidades diferentes.

Example The ratio 1 ft is a conversion factor.
12 in.

Coordinate plane (p. 60)  A plane formed by two number Plano de coordenadas (p. 60)  Se forma cuando dos rectas
lines that intersect at right angles. numéricas se cortan formando ángulos rectos.

Example 2 y-axis
Ϫ4
Ϫ2 O x-axis
24

Ϫ2

826

English Spanish

Coordinates (p. 60)  The numbers that make an ordered Coordenadas (p. 60)  Números ordenados por pares que
pair and identify the location of a point. determinan la posición de un punto sobre un plano.

Example y Visual Glossary

R 2 The coordinates of
T x R are (Ϫ4, 1).

Ϫ4 Ϫ2 O 2
UϪ2 S

Ϫ4

Correlation coefficient (p. 339)  A number from -1 to 1 Coeficiente de correlación (p. 339)  Número de - 1 a 1
that tells you how closely the equation of the line of best fit que indica con cuánta exactitud la línea de mejor encaje
models the data. representa los datos.

Example

LinReg
y = ax+b
a = .0134039132
b = –.3622031627
r2 = .886327776
r = .9414498267

The correlation coefficient is
approximately 0.94.

Cosine (p. 645)  In a right triangle, such as △ABC with Coseno (p. 645)  En un triángulo rectángulo tal que △ABC
right ∠C , con ∠C recto, el coseno de

cosine of ∠A = length of side adjacent to ∠A, or cos A = bc . ∠A = longitud del lado adyacente a ∠A , o cos A = b .
length of hypotenuse longitud de la hipotenusa c

Example A cos A ϭ 4
4 5

5

C 3B

Counterexample (p. 25)  An example showing that a Contraejemplo (p. 25)  Ejemplo que demuestra que un
statement is false. enunciado es falso.

Example Statement All apples are red.
Counterexample A Granny Smith apple is green.

Cross product (of sets) (p. 220)  The cross product of two Producto cruzado (de dos conjuntos) (p. 220)  El producto
sets A and B, denoted by A * B, is the set of all ordered cruzado de dos conjuntos A y B, definido por A * B, es el
pairs with the first element in A and with the second element conjunto de todos los pares ordenados cuyo primer elemento

in B. está en A y cuyo segundo elemento está en B.

Glossary i 827

English Spanish

Cross products (of a proportion) (p. 125)  In a proportion Productos cruzados (de una proporción) (p. 125)  En
a c a c
b = d , the products ad and bc. These products are equal. una proporción b = d , los productos ad y bc. Estos productos
son iguales.
Visual Glossary # #Example
The cross products for 3 = 6 are 3 8 and 4 6.
4 8

Cumulative frequency table (p. 734)  A table that shows Tabla de frecuencia cumulativa (p. 734)  Tabla que
the number of data values that lie in or below the given muestra el número de valores de datos que están dentro o
intervals. por debajo de los intervalos dados.

Example Frequency Cumulative
5 Frequency
Interval 8
4 5
0–9 13
10–19 17
20–29

D

Decay factor (p. 462)  1 minus the percent rate of change, Factor de decremento (p. 462)  1 menos la tasa
expressed as a decimal, for an exponential decay situation. porcentual de cambio, expresada como decimal, en una
situación de reducción exponencial.

Example The decay factor of the function
y = 5(0.3)x is 0.3.

Deductive reasoning (p. 25)  A process of reasoning Razonamiento deductivo (p. 25)  El razonamiento
logically from given facts to a conclusion. deductivo es un proceso de razonamiento lógico que parte
de hechos dados hasta llegar a una conclusión.

Example Based on the fact that the sum of
any two even numbers is even, you
can deduce that the product of any
whole number and any even
number is even.

Degree of a monomial (p. 486)  The sum of the exponents Grado de un monomio (p. 486)  La suma de los
of the variables of a monomial. exponentes de las variables de un monomio.

Example - 4x3y2 is a monomial of degree 5.

Degree of a polynomial (p. 487)  The highest degree of Grado de un polinomio (p. 487)  El grado de un
any term of the polynomial. polinomio es el grado mayor de cualquier término del
polinomio.

Example The polynomial P(x) = x6 + 2x3 - 3
has degree 6.

828

English Spanish

Dependent events (p. 778)  When the outcome of one Sucesos dependientes (p. 778)  Dos sucesos son Visual Glossary
event affects the probability of a second event, the events are dependientes si el resultado de un suceso afecta la
dependent events. probabilidad del otro.

Example You have a bag with marbles of different
colors. If you pick a marble from the bag
and pick another without replacing the first,
the events are dependent events.

Dependent system (p. 365)  A system of equations that Sistema dependiente (p. 365)  Sistema de ecuaciones que
does not have a unique solution. no tiene una solución única.

Example T he system e y = 2x +3 6 represents two
- 4x + 2y =
equations for the same line, so it has many

solutions. It is a dependent system.

Dependent variable (p. 240)  A variable that provides the Variable dependiente (p. 240)  Variable de la que
output values of a function. dependen los valores de salida de una función.

Example In the equation y = 3x, y is the
dependent variable.

Difference of squares (p. 525)  A difference of two Diferencia de dos cuadrados (p. 525)  La diferencia de
squares is an expression of the form a2 - b2. It can be dos cuadrados es una expresión de la forma a2 - b2. Se
factored as (a + b)(a - b). puede factorizar como (a + b)(a - b).

Examples 25a2 - 4 = (5a + 2)(5a - 2)
m6 - 1 = (m3 + 1)(m3 - 1)

Direct variation (p. 301)  A linear function defined by an Variación directa (p. 301)  Una función lineal definida por
equation of the form y = kx, where k ≠ 0. una ecuación de la forma y = kx, donde k ≠ 0, representa
una variación directa.

Example y = 18x is a direct variation.

Discrete graph (p. 255)  A graph composed of isolated Gráfica discreta (p. 255)  Una gráfica discreta es
points. compuesta de puntos aislados.

Example y
2

Ϫ2 O 2 x

Discriminant (p. 585)  The discriminant of a quadratic Discriminante (p. 585)  El discriminante de una ecuación
equation of the form ax2 + bx + c = 0 is b2 - 4ac. The cuadrática ax2 + bx + c = 0 es b2 - 4ac. El valor del
value of the discriminant determines the number of solutions discriminante determina el número de soluciones de la
of the equation. ecuación.

Example The discriminant of
2x2 + 9x - 2 = 0 is 97.

Glossary i 829

English Spanish

Disjoint sets (p. 215)  Sets that do not have any elements Conjuntos ajenos (p. 215)  Conjuntos que no tienen
in common. elementos en común.

Visual Glossary Example The set of positive integers and

the set of negative integers are

disjoint sets.

Distributive Property (p. 46)  For every real number a, b, Propiedad Distributiva (p. 46)  Para cada número real a, b
and c: y c:

a(b + c) = ab + ac (b + c)a = ba + ca a(b + c) = ab + ac (b + c)a = ba + ca
a(b - c) = ab - ac (b - c)a = ba - ca a(b - c) = ab - ac (b - c)a = ba - ca

Examples 3(19 + 4) = 3(19) + 3(4)
(19 + 4)3 = 19(3) + 4(3)
7(11 - 2) = 7(11) - 7(2)
(11 - 2)7 = 11(7) - 2(7)

Domain (of a relation or function) (p. 268)  The possible Dominio (de una relación o función) (p. 268) Posibles
values for the input of a relation or function. valores de entrada de una relación o función.

Example In the function f (x) = x + 22, the

domain is all real numbers.

E

Element (of a matrix) (p. 726)  An item in a matrix. Elemento (de una matriz) (p. 726)  Componente de una
matriz.

Example 5 -2 R
J7 3

5, 7, - 2, and 3 are the four
elements of the matrix.

Elements (of a set) (p. 17)  Members of a set. Elementos (p. 17)  Partes integrantes de un conjunto.

Example Cats and dogs are elements of the
set of mammals.

Elimination method (p. 378)  A method for solving a Eliminación (p. 378)  Método para resolver un sistema de
system of linear equations. You add or subtract the equations ecuaciones lineales. Se suman o se restan las ecuaciones para
to eliminate a variable. eliminar una variable.

Example 3x + y = 19 Add the equations to get x = 4.
2x - y = 1
5x + 0 = 20

2(4) - y = 1  S Substitute 4 for x in
8 - y = 1 the second equation.

y = 7  S Solve for y.

Empty set (p. 195)  A set that does not contain any Conjunto vacío (p. 195)  Conjunto que no contiene
elements. elementos.

Example The intersection of the set of
positive integers and the set of
negative integers is the empty set.

830

English Spanish

Equation (p. 53)  A mathematical sentence that uses an Ecuación (p. 53)  Enunciado matemático que tiene el signo
equal sign. de igual.

Example x + 5 = 3x - 7 Visual Glossary

Equivalent equations (p. 81)  Equations that have the Ecuaciones equivalentes (p. 81)  Ecuaciones que tienen la
same solution. misma solución.

Example e93q=ui3vaalenndt93eq+uaat=io3ns+. a are

Equivalent expressions (p. 23)  Algebraic expressions that Expresiones equivalentes (p. 23)  Expresiones algebraicas
have the same value for all values of the variable(s). que tienen el mismo valor para todos los valores de la(s)
variable(s).

Example 3a + 2a and 5a are equivalent
expressions.

Equivalent inequalities (p. 171)  Inequalities that have the Desigualdades equivalentes (p. 171)  Las desigualdades
same set of solutions. equivalentes tienen el mismo conjunto de soluciones.

Example x + 4 6 7 and x 6 3 are

equivalent inequalities.

Evaluate (p. 12)  To substitute a given number for each Evaluar (p. 12)  Método de sustituir cada variable por un
variable, and then simplify. número dado para luego simplificar la expresión.

Example To evaluate 3x + 4 for x = 2,
substitute 2 for x and simplify.
3(2) + 4 = 6 + 4 = 10

Event (p. 769)  Any group of outcomes in a situation Suceso (p. 769)  En la probabilidad, cualquier grupo de
involving probability. resultados.

Example When rolling a number cube, there
are six possible outcomes. Rolling an
even number is an event with three
possible outcomes, 2, 4, and 6.

Excluded value (p. 664)  A value of x for which a rational Valor excluido (p. 664)  Valor de x para el cual una
expression f (x) is undefined. expresión racional es indefinida.

Experimental probability (p. 771)  The ratio of the Probabilidad experimental (p. 771)  La razón entre el

number of times an event actually happens to the number número de veces que un suceso sucede en la realidad y el
of times the experiment is done.
número de veces que se hace el experimento.

P(event) = number of times an event happens P(suceso) = nu´mero de veces que sucede un suceso
number of times the experiment is done nu´ mero de veces que se hace el experimento

Example A baseball player’s batting average
shows how likely it is that a player
will get a hit, based on previous
times at bat.

Glossary i 831

English Spanish

Explicit formula (p. 276)  An explicit formula expresses the Fórmula explícita (p. 276)  Una fórmula explícita expresa
nth term of a sequence in terms of n. el n-ésimo término de una progresión en función de n.

Visual Glossary Example Let an = 2n + 5 for positive
integers n. If n = 7, then
a7 = 2(7) + 5 = 19.

Exponent (p. 10)  A number that shows repeated Exponente (p. 10)  Denota el número de veces que debe

multiplication. # # #multiplicarse.

Example 34 = 3 3 3 3
The exponent 4 indicates that 3 is

used as a factor four times.

Exponential decay (p. 462)  A situation modeled with a Decremento exponencial (p. 462) Para a 7 0 y
function of the form y = abx, where a 7 0 and 0 6 b 6 1. 0 6 b 6 1, la función y = abx representa el decremento
exponencial.
Example y = 5(0.1)x

Exponential function (p. 453)  A function that repeatedly Función exponencial (p. 453)  Función que multiplica
multiplies an initial amount by the same positive number. You repetidas veces una cantidad inicial por el mismo número
can model all exponential functions using y = abx, where a positivo. Todas las funciones exponenciales se pueden
is a nonzero constant, b 7 0, and b ≠ 1. representar mediante y = abx, donde a es una constante con
valor distinto de cero, b 7 0 y b ≠ 1.

Example y

exponential 4 exponential
decay 2 growth
y ‫ ؍‬2x
y ‫ ؍‬0.5x

Ϫ4 Ϫ2 O 2 4 x

Exponential growth (p. 460)  A situation modeled with a Incremento exponencial (p. 460) Para a 7 0 y b 7 1, la
function of the form y = abx, where a 7 0 and b 7 1. función y = abx representa el incremento exponencial.

Example y = 100(2)x

Extraneous solution (p. 635)  A solution of an equation Solución extraña (p. 635)  Una solución extraña es una
derived from an original equation that is not a solution of the solución de una ecuación derivada que no es una solución
original equation. de la ecuación original.

Example b b 4 = 3 - b 4 4
+ +

b = 3(b + 4) - 4 Multiply by (b + 4).

b = 3b + 12 - 4
-2b = 8
  b = -4

R eplace b with - 4 in the original
equation. The denominator is 0, so
- 4 is an extraneous solution.

832

English Spanish

Extrapolation (p. 337)  The process of predicting a value Extrapolación (p. 337)  Proceso que se usa para predecir
outside the range of known values. un valor por fuera del ámbito de los valores dados.

F Visual Glossary

Factor by grouping (p. 529)  A method of factoring that Factor común por agrupación de términos
uses the Distributive Property to remove a common binomial (p. 529)  Método de factorización que aplica la propiedad
factor of two pairs of terms. distributiva para sacar un factor común de dos pares de
términos en un binomio.

Example T he expression

7x(x - 1) + 4(x - 1) can be
factored as (7x + 4)(x - 1).

Formula (p. 110)  An equation that states a relationship Fórmula (p. 110)  Ecuación que establece una relación
among quantities. entre cantidades.

Example The formula for the volume V of a
cylinder is V = pr2h, where r is the
radius of the cylinder and h is its
height.

Frequency (p. 732)  The number of data items in an Frecuencia (p. 732)  Número de datos de un intervalo.
interval.

Example In the data set 4, 7, 12, 4, 5, 8, 11,

2, the frequency of the interval 5–9

is 3.

Frequency table (p. 732)  A table that groups a set of data Tabla de frecuencias (p. 732)  Tabla que agrupa un
values into intervals and shows the frequency for each conjunto de datos en intervalos y muestra la frecuencia
interval. de cada intervalo.

Example
Interval Frequency

0–9 5

10–19 8

20–29 4

Function (p. 241)  A relation that assigns exactly one value Función (p. 241)  La relación que asigna exactamente un
in the range to each value of the domain. valor del rango a cada valor del dominio.

Example E arned income is a function of the

number of hours worked. If you

earn $4.50/h, then your income is

expressed by the function
f (h) = 4.5h.

Function notation (p. 269)  To write a rule in function Notación de una función (p. 269)  Para expresar una regla
notation, you use the symbol f (x) in place of y. en notación de función se usa el símbolo f (x) en lugar de y.

Example f (x) = 3x - 8 is in function

notation.

Glossary i 833

English Spanish

Function rule (p. 262)  An equation that describes a Regla de función (p. 262)  Ecuación que describe una
function. función.

Example y = 4x + 1 is a function rule.

G
Visual Glossary
Geometric sequence (p. 467)  A number sequence formed Progresión geométrica (p. 467)  Tipo de sucesión
Frequencyby multiplying a term in a sequence by a fixed number to findnumérica formada al multiplicar un término de la secuencia
the next term. por un número constante, para hallar el siguiente término.

Example 9, 3, 1, 13, . . . is an example of a

geometric sequence.

Growth factor (p. 460)  1 plus the percent rate of change Factor incremental (p. 460)  1 más la tasa porcentual de
for an exponential growth situation. cambio en una situación de incremento exponencial.

Example The growth factor of y = 7(1.3)x

is 1.3.

H

Histogram (p. 733)  A special type of bar graph that can Histograma (p. 733)  Tipo de gráfica de barras que
display data from a frequency table. Each bar represents an muestra los datos de una tabla de frecuencia. Cada barra
interval. The height of each bar shows the frequency of the representa un intervalo. La altura de cada barra muestra la
interval it represents. frecuencia del intervalo al que representa.

Example 10

8

6

4

2

0 0–9 10–19 20–29
Interval

Hypotenuse (p. 614)  The side opposite the right angle in a Hipotenusa (p. 614)  En un triángulo rectángulo, el lado
right triangle. It is the longest side in the triangle. opuesto al ángulo recto. Es el lado más largo del triángulo.

Example A c is the hypotenuse.
c
b

C aB

Hypothesis (p. 615)  In an if-then statement (conditional), Hipótesis (p. 615)  En un enunciado si. . . entonces. . .
the hypothesis is the part that follows if. (condicional), la hipótesis es la parte del enunciado que sigue
el si.

Example In the conditional “If an animal has
four legs, then it is a horse,” the
hypothesis is “an animal has four
legs.”

834

English Spanish

I

Identity (p. 104)  An equation that is true for every value. Identidad (p. 104)  Una ecuación que es verdadera para
todos los valores.
Visual Glossary
( )Example i1t54isx
5 - 14x =5 1- is an any
identity because true for

value of x.

Inconsistent system (p. 365)  A system of equations that Sistema incompatible (p. 365)  Un sistema incompatible
has no solution. es un sistema de ecuaciones para el cual no hay solución.

Example e y- =2x2+x + 3 1 is a system of
y =

parallel lines, so it has no solution.

It is an inconsistent system.

Independent events (p. 777)  When the outcome of one Sucesos independientes (p. 777)  Cuando el resultado de
event does not affect the probability of a second event, the un suceso no altera la probabilidad de otro, los dos sucesos
two events are independent. son independientes.

Example The results of two rolls of a
number cube are independent.
Getting a 5 on the first roll does
not change the probability of
getting a 5 on the second roll.

Independent system (p. 365)  A system of linear Sistema independiente (p. 365)  Un sistema de ecuaciones
equations that has a unique solution. lineales que tenga una sola solución es un sistema independiente.

Example ex2x+-23y y==-07 has the unique
solution ( - 3, - 2). It is an
independent system.

Independent variable (p. 240)  A variable that provides Variable independiente (p. 240)  Variable de la que
the input values of a function. dependen los valores de entrada de una función.

Example In the equation y = 3x, x is the
independent variable.

Index (p. 448)  With a radical sign, the index indicates the Índice (p. 448)  Con un signo de radical, el índice indica el
degree of the root. grado de la raíz.

Example index 2   index 3   index 4
116   23 16 24 16

Inductive reasoning (p. 63)  Making conclusions based on Razonamiento inductivo (p. 63)  Sacar conclusiones a
observed patterns. partir de patrones observados.

Inequality (p. 19)  A mathematical sentence that compares Desigualdad (p. 19)  Expresión matemática que compara el
the values of two expressions using an inequality symbol. valor de dos expresiones con el símbolo de desigualdad.

Example 3 6 7

Glossary i 835

English Spanish

Input (p. 240)  A value of the independent variable. Entrada (p. 240)  Valor de una variable independiente.

Visual Glossary Example The input is any value of x you
substitute into a function.

Integers (p. 18)  Whole numbers and their opposites. Números enteros (p. 18)  Números que constan
exclusivamente de una o más unidades, y sus opuestos.

Example c - 3, - 2, - 1, 0, 1, 2, 3, c

Interpolation (p. 337)  The process of estimating a value Interpolación (p. 337)  Proceso que se usa para estimar el
between two known quantities. valor entre dos cantidades dadas.

Interquartile range (p. 746)  The interquartile range of a Intervalo intercuartil (p. 746)  El rango intercuartil de un
set of data is the difference between the third and first conjunto de datos es la diferencia entre el tercero y el primer
quartiles. cuartiles.

Example The first and third quartiles of the

data set 2, 3, 4, 5, 5, 6, 7, and 7

are 3.5 and 6.5. The interquartile
range is 6.5 - 3.5 = 3.

Intersection (p. 215)  The set of elements that are common Intersección (p. 215)  El conjunto de elementos que son
to two or more sets. comunes a dos o más conjuntos.

Example I f C = 51, 2, 3, 46 and
D = 52, 4, 6, 86, then the
intersection of C and D, or
C ¨ D, is {2, 4}.

Interval notation (p. 203)  A notation for describing an Notación de intervalo (p. 203)  Notación que describe un
interval on a number line. The interval’s endpoint(s) are intervalo en una recta numérica. Los extremos del intervalo se
given, and a parenthesis or bracket is used to indicate incluyen y se usa un paréntesis o corchete para indicar si cada
whether each endpoint is included in the interval. extremo está incluido en el intervalo.

Example For -2 … x 6 8, the interval
notation is [ - 2, 8).

Inverse function (p. 329)  If function f pairs a value b with Funcion inversa (p. 329)  Si la función f empareja un valor
a then its inverse, denoted f -1, pairs the value a with b. If b con a, entonces su inversa, cuya notación es f -1, empareja
f -1 is also a function, then f and f -1 are inverse functions. el valor a con b. Si f -1 también es una función, entonces f y
f -1 son funciones inversas.

Example If f (x) = x + 3, then
f -1(x) = x - 3.

Inverse operations (p. 82)  Operations that undo Operaciones inversas (p. 82)  Las operaciones que se
one another. cancelan una a la otra.

Example Addition and subtraction are
inverse operations. Multiplication
and division are inverse operations.

836

English Spanish

Inverse variation (p. 692)  An equation of the form Variación inversa (p. 692)  La ecuación y = kx , ó xy = k,
k ≠ donde k ≠ 0, es una variación inversa con una constante de
xy = k or y = x , where k 0, is an inverse variation with variación k.

constant of variation k. Visual Glossary

Example T he length x and the width y of a

rectangle with a fixed area vary
inversely. If the area is 40, xy = 40.

Irrational number (p. 18)  A number that cannot be Número irracional (p. 18)  Número que no puede
written as a ratio of two integers. Irrational numbers in expresarse como razón de dos números enteros. Los números
decimal form are nonterminating and nonrepeating. irracionales en forma decimal no tienen término y no se
repiten.

Example 111 and p are irrational numbers.

Isolate (p. 82)  Using properties of equality and inverse Aislar (p. 82)  Usar propiedades de igualdad y operaciones
operations to get a variable with a coefficient of 1 alone on inversas para poner una variable con un coeficiente de 1 sola
one side of the equation. a un lado de la ecuación.

Example x + 3 = 7
x+3-3=7-3
x=4

L

Leg (p. 614)  Each of the sides that form the right angle of Cateto (p. 614)  Cada uno de los dos lados que forman el
a right triangle. ángulo recto en un triángulo rectángulo.

Example A c a and b are legs.
b

Ca B

Like radicals (p. 626)  Radical expressions with the same Radicales semejantes (p. 626)  Expresiones radicales con
radicands. los mismos radicandos.

Example 317 and 2517 are like radicals.

Like terms (p. 48)  Terms with exactly the same variable Términos semejantes (p. 48)  Términos con los mismos
factors in a variable expression. factores variables en una expresión variable.

Example 4y and 16y are like terms.

Linear equation (p. 308)  An equation whose graph forms Ecuación lineal (p. 308)  Ecuación cuya gráfica es una línea
a straight line. recta.

Example y y ‫ ؍‬2x ؉ 1
Ϫ4 x
1

Ϫ2 O 2 4

Ϫ2

Glossary i 837

English Spanish

Visual Glossary Linear function (p. 241)  A function whose graph is a line Función lineal (p. 241)  Una función cuya gráfica es una
is a linear function. You can represent a linear function with a recta es una función lineal. La función lineal se representa
linear equation. con una ecuación lineal.

Example y

2 y ‫ ؍‬2x ؉ 1

Ϫ2 2 x

Linear inequality (p. 394)  An inequality in two variables Desigualdad lineal (p. 394)  Una desigualdad lineal es una
whose graph is a region of the coordinate plane that is desigualdad de dos variables cuya gráfica es una región del
bounded by a line. Each point in the region is a solution of plano de coordenadas delimitado por una recta. Cada punto
the inequality. de la región es una solución de la desigualdad.

Example 2y
yϾx؉1
x
Ϫ2 O
2
Ϫ2

Linear parent function (p. 308)  The simplest form of a Función lineal elemental (p. 308)  La forma más simple de
linear function. una función lineal.

Example y = x

Line of best fit (p. 339)  The most accurate trend line on Recta de mayor aproximación (p. 339)  La línea de
a scatter plot showing the relationship between two sets tendencia en un diagrama de puntos que más se acerca a los
of data. puntos que representan la relación entre dos conjuntos de datos.

Example Calories and Fat for
Fast Food Meals

600

Calories 400

200 10 20 30 40 50
0 Fat (g)
0

Literal equation (p. 109)  An equation involving two or Ecuación literal (p. 109)  Ecuación que incluye dos o más
more variables. variables.

Example 4x + 2y = 18 is a literal equation.

838

English Spanish

M Matriz (p. 726)  Una matriz es un conjunto de números Visual Glossary

Matrix (p. 726)  A matrix is a rectangular array of numbers encerrados en corchetes y dispuestos en forma de rectángulo.
written within brackets. A matrix with m horizontal rows and Una matriz que contenga m filas y n columnas es una
n vertical columns is an m * n matrix. matriz m * n.

Example 2 5 6.3 is a 2 * 3 matrix.
J -8 0 -1R

Maximum (p. 547)  The y-coordinate of the vertex of a Máximo (p. 547)  La coordenada y del vértice en una
parabola that opens downward. parábola que se abre hacia abajo.

Example y x
Ϫ2 O 2

Since the parabola opens
downward, the y-coordinate
of the vertex is the function’s
maximum value.

Mean (p. 738)  To find the mean of a set of data values, Media (p. 738)  Para hallar la media de un conjunto de

find the sum of the data values and divide the sum by the datos, halla la suma de los valores de los datos y divide la
sum of the odfatdaatvaalvuaelsues. suma por el total del valor de los datos. La media es
number of data values. The mean is total number

el la suma de los datos datos .
nu´ mero total de valores de

Example In the data set 12, 11, 12, 10, 13,

12, and 7, the mean is

12 + 11 + 12 + 10 + 13 + 12 + 7 = 11.
7

Measure of central tendency (p. 738)  Mean, median, Medida de tendencia central (p. 738)  La media, la
and mode. They are used to organize and summarize a set mediana y la moda. Se usan para organizar y resumir un
of data. conjunto de datos.

Example For examples, see mean, median,
and mode.

Measure of dispersion (p. 740)  A measure that describes Medida de dispersión (p. 740)  Medida que describe
how dispersed, or spread out, the values in a data set are. cómo se dispersan, o esparecen, los valores de un conjunto
Range is a measure of dispersion. de datos. La amplitud es una medida de dispersión.

Example For an example, see range.

Median (p. 738)  The middle value in an ordered set of Mediana (p. 738)  El valor del medio en un conjunto
numbers. ordenado de números.

Example In the data set 7, 10, 11, 12, 12,
12, and 13, the median is 12.

Glossary i 839

English Spanish

Midpoint (p. 114)  The point M that divides a segment AB Punto medio (p. 114)  El punto M que divide un segmento
into two equal segments, AM and MB. AB en dos segmentos iguales, AM y MB.

Visual Glossary Example M is the midpoint of XY.

XMY

Midpoint Formula (p. 114)  The midpoint M of a line Fórmula del punto medio (p. 114)  El punto medio M de

segment with endpoints A(x1, y1) and B(x2, y2) is un segmento con puntos extremos A(x1, y1) y B(x2, y2) es

¢ x1 + x2, y1 + y2 ≤. ¢ x1 + x2, y1 + y2 ≤.
2 2 2 2

Example The midpoint of a segment with
endpoints A(3, 5) and B(7, 1)
is (5, 3).

Minimum (p. 547) The y-coordinate of the vertex of a Mínimo (p. 547)  La coordenada y del vértice en una
parabola that opens upward. parábola que se abre hacia arriba.

Example 2y

Ϫ2 O x
2

Ϫ2

Since the parabola opens upward,
the y-coordinate of the vertex is
the function’s minimum value.

Mode (p. 738)  The mode is the most frequently occurring Moda (p. 738)  La moda es el valor o valores que ocurren
value (or values) in a set of data. A data set may have no con mayor frequencia en un conjunto de datos. El conjunto
mode, one mode, or more than one mode. de datos puede no tener moda, o tener una o más modas.

Example In the data set 7, 7, 9, 10, 11, and
13, the mode is 7.

Monomial (p. 486)  A real number, a variable, or a product Monomio (p. 486)  Número real, variable o el producto de
of a real number and one or more variables with whole- un número real y una o más variables con números enteros
number exponents. como exponentes.

Example 9, n, and - 5xy2 are examples of
monomials.

Multiplication Counting Principle (p. 763)  If there are Principio de Conteo en la Multiplicación (p. 763)  Si hay

m ways to make the first selection and n ways to make the m maneras de hacer la primera selección y n maneras de
second selection, then there are m ⋅ n ways to make the hacer la segunda selección, quiere decir que hay m ⋅ n
two selections. maneras de hacer las dos selecciones.

Example For 5 shirts and 8 pairs of shorts,
the number of possible outfits is
5 ⋅ 8 = 40.

840

English Spanish

Multiplicative inverse (p. 40)  Given a nonzero rational Inverso multiplicativo (p. 40)  Dado un nreúcmíperroocora,ceios nbaa.lEbal
oba f, b distinto de cero, el inverso multiplicativo, o
number the multiplicative inverse, or reciprocal, is a . The
product
a nonzero number and its multiplicative inverse producto de un número distinto de cero y su inverso Visual Glossary

is 1. multiplicativo es 1.

Example b34eicsatuhseem43u*lti43pl=ica1t.ive inverse of 3
4

Mutually exclusive events (p. 776)  When two events Sucesos mutuamente excluyentes (p. 776)  Cuando dos

cannot happen at the same time, the events are mutually sucesos no pueden ocurrir al mismo tiempo, son
exclusive. If A and B are mutually exclusive events, then mutuamente excluyentes. Si A y B son sucesos mutuamente
P(A or B) = P(A) + P(B). excluyentes, entonces P(A o B) = P(A) + P(B).

Example Rolling an even number E and
rolling a multiple of five M on a
standard number cube are
mutually exclusive events.

P(E or M) = P(E) + P(M)

= 3 + 1
6 6

= 4
6

= 2
3

N

Natural numbers (p. 18)  The counting numbers. Números naturales (p. 18)  Los números que se emplean
para contar.

Example 1, 2, 3, c

Negative correlation (p. 336)  The relationship between Correlación negativa (p. 336)  Relación entre dos
two sets of data, in which one set of data decreases as the conjuntos de datos en la que uno de los conjuntos disminuye
other set of data increases. a medida que el otro aumenta.

Example

0

Negative square root (p. 39)  A number of the form - 1b, Raíz cuadrada negativa (p. 39)  - 1b es la raíz cuadrada
which is the negative square root of b. negativa de b.

Example -7 is the negative square root of
149.

n factorial (p. 764)  The product of the integers from n n factorial (p. 764)  Producto de todos los enteros desde n
down to 1, for any positive integer n. You write n factorial as hasta 1, de cualquier entero positivo n. El factorial de n se
n!. The value of 0! is defined to be 1. escribe n!. El valor de 0! se define como 1.

Example 4! = 4 * 3 * 2 * 1 = 24

Glossary i 841

English Spanish

No correlation (p. 336)  There does not appear to be a Sin correlación (p. 336)  No hay relación entre dos
relationship between two sets of data. conjuntos de datos.

Visual Glossary Example

0

Nonlinear function (p. 246)  A function whose graph is Función no lineal (p. 246)  Función cuya gráfica no es una
not a line or part of a line. línea o parte de una línea.

Example y
2

Ϫ2 O 2x
Ϫ2

Normal distribution (p. 783)  A normal distribution shows Distribución normal (p. 783)  Una distribución normal
data that vary randomly from the mean in the pattern of a muestra, con una curva en forma de campana, datos que
bell-shaped curve. varían alcatoriamento respecto de la media.

Example Distribution of Test Scores

13.5% 13.5%
2.5% 34% 34% 2.5%

53.5 60.0 66.5 73.0 79.5

Null set (p. 195)  A set that has no elements. IInnaacclalsassosfo2f0200s0tusdteundtse,nthtse,stchoeresscores
sTooTthnnahenaeadmtmateeresdaetsnatdwsnewecvroesiearcretneiooowrnnreamowswra6amlals6ys.6ad5.6li5sla6yt.nr.Ti5ddbhuiateshtnteerddi.btuhteed.
nsutamnbdear rodf sdtuedveinattsiownhowsacsor6e.d5.gTrehaeter
tnhuanm7b3epreorcfesnttuwdaesnatbsowuht 1o3s.5c%ore1d2g.5re%atoefr
tthhoasne w73howtaooskatbhoeuttes1t3. .5% ϩ 2.5% of
1th6%oseofw2h00o 5to3o2k the test.
oAA1n6bbo%tohuuetot3tfe322s20ts.ts0utdϭuedn3et2snstcsosrecdor7e3do7r 3hioghrehrigher

on the test. Conjunto vacío (p. 195)  Conjunto que no tiene
elementos.

Example { } or Ø

Numerical expression (p. 4)  A mathematical phrase Expresión numérica (p. 4)  Frase matemática que contiene
involving numbers and operation symbols, but no variables. números y operaciones con símbolos, pero no variables.

Example 2 + 4

842

English Spanish

O

Odds (p. 771)  A ratio that compares the number of Probabilidad a favor (p. 771)  Razón que compara el Visual Glossary
favorable and unfavorable outcomes. Odds in favor are número de resultados favorables y no favorables. Las
number of favorable outcomes : number of unfavorable posibilidades a favor son el número de resultados favorables :
outcomes. Odds against are number of unfavorable número de resultados no favorables. Las posibilidades en
outcomes : number of favorable outcomes. contra son el número de resultados no favorables : número
de resultados favorables.

Example You have 3 red marbles and 5 blue
marbles. The odds in favor of
selecting red are 3 : 5.

Open sentence (p. 53)  An equation that contains one or Enunciado abierto (p. 53)  Una ecuación es un enunciado
more variables and may be true or false depending on the abierto si contiene una o más variables y puede ser verdadera
value of its variables. o falsa dependiendo del valor de sus variables.

Example 5 + x = 12 is an open sentence.

Opposite (p. 32)  A number that is the same distance from Opuestos (p. 32)  Dos números son opuestos si están a la
zero on the number line as a given number, but lies in the misma distancia del cero en la recta numérica, pero en
opposite direction. sentido opuesto.

Example -3 and 3 are opposites.

Opposite reciprocals (p. 331)  A number of the form - b , Recíproco inverso (p. 331)  Número en la forma - b ,
nwuhmerbeebar a ddeonudnenbaúmeseuron a
is a nonzero rational number. The product of a número racional diferente de cero. El producto
and its opposite reciprocal is - 1. y su recíproco inverso es - 1.

Example 2 and - 5 are opposite reciprocals
5 2
12521 - 5
because 2 2 = -1.

Ordered pair (p. 60)  Two numbers that identify the Par ordenado (p. 60)  Un par ordenado de números que
location of a point. denota la ubicación de un punto.

Example The ordered pair (4, -1) identifies
the point 4 units to the right on
the x-axis and 1 unit down on the
y-axis.

Order of operations (p. 11)  Orden de las operaciones (p. 11) 

  1.  Perform any operation(s) inside grouping symbols.   1.  Se hacen las operaciones que están dentro de símbolos

  2.  Simplify powers. de agrupación.

  3.  Multiply and divide in order from left to right.   2.  Se simplifican todos los términos que tengan exponentes.

  4.  Add and subtract in order from left to right.   3.  Se hacen las multiplicaciones y divisiones en orden de

izquierda a derecha.

  4.  Se hacen las sumas y restas en orden de izquierda a

# derecha.

Example 6 - (42 - [2 5]) , 3

= 6 - (16 - 10) , 3

=6-6,3

=6-2

=4

Glossary i 843

English Spanish

Origin (p. 60)  The point at which the axes of the Origen (p. 60)  Punto de intersección de los ejes del plano
coordinate plane intersect. de coordenadas.

Visual Glossary Example y-axis

2 x-axis
2
Ϫ2 O
Ϫ2 origin

Outcome (p. 769)  The result of a single trial in a probability Resultado (p. 769)  Lo que se obtiene al hacer una sola
experiment. prueba en un experimento de probabilidad.

Example The outcomes of rolling a number
cube are 1, 2, 3, 4, 5, and 6.

Outlier (p. 738)  An outlier is a data value that is much Valor extremo (p. 738)  Un valor extremo es el valor de un
higher or lower than the other data values in the set. dato que es mucho más alto o mucho más bajo que los otros
valores del conjunto de datos.

Example For the set of values 2, 5, 3, 7, 12,
the data value 12 is an outlier.

Output (p. 240)  A value of the dependent variable. Salida (p. 240)  Valor de una variable dependiente.

Example The output of the function
f(x) = x2 when x = 3 is 9.

Overlapping events (p. 776)  Events that have at least one Sucesos traslapados (p. 776)  Sucesos que tienen por lo

common outcome. If A and B are overlapping events, then menos un resultado en común. Si A y B son sucesos
P(A or B) = P(A) + P(B) - P(A and B). traslapados, entonces P(A ó B) = P(A) + P(B) - P(A y B).

Example Rolling a multiple of 3 and rolling
an odd number on a number cube
are overlapping events.

P(multiple of 3 or odd) = P(multiple of 3) + P(odd) - P(multiple of 3 and odd) 

= 1 + 1 - 1
3 2 6
2
  = 3

P

Parabola (p. 546)  The graph of a quadratic function. Parábola (p. 546)  La gráfica de una función cuadrática.

Example y
Ox

844

English Spanish

Parallel lines (p. 330)  Two lines in the same plane that Rectas paralelas (p. 330)  Dos rectas situadas en el mismo
never intersect. Parallel lines have the same slope. plano que nunca se cortan. Las rectas paralelas tienen la
misma pendiente.
Visual Glossary
Example yℓ
m

Ox

Parent function (p. 308)  A family of functions is a group Función elemental (p. 308)  Una familia de funciones es
of functions with common characteristics. A parent function un grupo de funciones con características en común. La
is the simplest function with these characteristics. función elemental es la función más simple que reúne esas
características.

Example y = x is the parent function for
the family of linear equations of
the form y = mx + b.

Percent change  (p. 144)  The ratio of the amount of Cambio porcentual (p. 144)  La razón de la cantidad de
change to the original amount expressed as a percent. cambio y la cantidad original, expresada como un porcentaje.

Example The price of a sweater was $20.

The price increases $2. The percent
2
change is 20 = 10%.

Percent decrease (p. 144)  The percent change found Disminución porcentual (p. 144)  Cambio porcentual que
when the original amount decreases. se encuentra cuando la cantidad original disminuye.

Example The price of a sweater was $22.

The price decreases $2. The
2 ≈
percent change is 22 9%.

Percent error (p. 146)  The ratio of the absolute value of Error porcentual (p. 146)  Razón del valor absoluto de la
the difference of the measured (or estimated) value and an diferencia de un valor medido (o estimado) y un valor actual
actual value compared to the actual value, expressed as a en comparación con el valor actual, expresada como un
percent. porcentaje.

Example The diameter of a CD is measured

as 12.1 cm. The greatest possible

error is 0.05 cm. The percent error

is 0.05 ≈ 0.4%.
12.1

Percentile (p. 749)  A value that separates a data set into Percentil (p. 749)  Valor que separa el conjunto de datos en
100 equal parts. 100 partes iguales.

Percentile rank (p. 749)  The percentage of data values Rango percentil (p. 749)  Porcentaje de valores de datos
that are less than or equal to a given value. que es menos o igual a un valor dado.

Percent increase (p. 144)  The percent change found when Aumento porcentual (p. 144)  Cambio porcentual que se
the original amount increases. encuentra cuando la cantidad original aumenta.

Glossary i 845

English Spanish

Perfect squares (p. 17)  Numbers whose square roots Cuadrado perfecto (p. 17)  Número cuya raíz cuadrada es
are integers. un número entero.

Visual Glossary Example The numbers 1, 4, 9, 16, 25, 36, . . .
are perfect squares because they
are the squares of integers.

Perfect square trinomial (p. 523)  Any trinomial of the Trinomio cuadrado perfecto (p. 523)  Todo trinomio de la
form a2 + 2ab + b2 or a2 - 2ab + b2. forma a2 + 2ab + b2 ó a2 - 2ab + b2.

Example (x + 3)2 = x2 + 6x + 9

Permutation (p. 763)  An arrangement of some or all of a Permutación (p. 763)  Disposición de algunos o de todos
set of objects in a specific order. You can use the notation nPr los objetos de un conjunto en un orden determinado. El
to express the number of permutations, where n equals the número de permutaciones se puede expresar con la
number of objects available and r equals the number of notación nPr, donde n es igual al número total de objetos y r
selections to make. es igual al número de selecciones que han de hacerse.

Example How many ways can you arrange

# # # # #5 objects 3 at a time? 5
5P3 = (5 5! = 5! = 432 1 = 60
- 3)! 2! 21

There are 60 ways to arrange
5 objects 3 at a time.

Perpendicular lines (p. 331)  Lines that intersect to form Rectas perpendiculares (p. 331)  Rectas que forman
ángulos rectos en su intersección. Dos rectas son
right angles. Two lines are perpendicular if the product of perpendiculares si el producto de sus pendientes es - 1.
their slopes is - 1.
m
Example ℓ y x

Piecewise function (p. 348)  A piecewise function has Función de fragmentos (p. 348)  Una función de
different rules for different parts of its domain. fragmentos tiene reglas diferentes para diferentes partes de
su dominio.

Point-slope form (p. 315)  A linear equation of a Forma punto-pendiente (p. 315)  La ecuación lineal de
nonvertical line written as y - y1 = m(x - x1). The line una recta no vertical que pasa por el punto (x1, y1) con
passes through the point (x1, y1) with slope m. pendiente m está dada por y - y1 = m(x - x1).

Example An equation with a slope of - 1
2
passing through (2, -1) would be
written y + 1= - 1 -
point-slope form. 2 (x 2) in

846

English Spanish

Polynomial (p. 487)  A monomial or the sum or difference Polinomio (p. 487)  Un monomio o la suma o diferencia de Visual Glossary
of two or more monomials. A quotient with a variable in the dos o más monomios. Un cociente con una variable en el
denominator is not a polynomial. denominador no es un polinomio.

Example 2x2, 3x + 7, 28, and
- 7x3 - 2x2 + 9 are all
polynomials.

Population (p. 754)  The entire group that you are Población (p. 754)  El grupo entero del cual juntas
collecting information about. información.

Positive correlation (p. 336)  The relationship between Correlación positiva (p. 336)  La relación entre dos
two sets of data in which both sets of data increase together. conjuntos de datos en la que ambos conjuntos incrementan
a la vez.
Example

0

Power (p. 10)  The base and the exponent of an expression Potencia (p. 10)  La base y el exponente de una expresión
of the form an. de la forma an.

Principal square root (p. 16)  A number of the form 1b. Raíz cuadrada principal (p. 16)  La expresión 1b se llama
The expression 1b is called the principal (or positive) square raíz cuadrada principal (o positiva) de b.
root of b.

Example 5 is the principal square
root of 125.

Probability (p. 769)  How likely it is that an event will occur Probabilidad (p. 769)  La posibilidad de que un suceso
(written formally as P(event)). ocurra, escrita formalmente P(suceso).

Example You have 4 red marbles and

3 white marbles. The probability

that you select one red marble,

and then, without replacing it,

#randomly select another red=43 = 72.
marble is P(red) 7 6

Properties of equality (p. 81)  For all real numbers a, b, Propiedades de la igualdad (p. 81)  Para todos los

and c: números reales a, b y c:

  Addition: If a = b, then a + c = b + c.   Suma: Si a = b, entonces a + c = b + c.
  Subtraction: If a = b, then a - c = b - c. # #  Resta: Si a = b, entonces a - c = b - c.

# #  Multiplication: If a = b, then a c = b c.   Multiplicación: Si a = b, entonces a c = b c.
a b a b
  Division: If a = b, and c ≠ 0, then c = c .   División: Si a = b, y c ≠ 0, entonces c = c .

Glossary i 847

English Spanish

Proportion (p. 124)  An equation that states that two Proporción (p. 124)  Es una ecuación que establece que
ratios are equal. dos razones son iguales.

Visual Glossary Example 7.5 = 5
9 6

Pythagorean Theorem (p. 614)  In any right triangle, the Teorema de Pitágoras (p. 614)  En un triángulo
sum of the squares of the lengths of the legs is equal to the rectángulo, la suma de los cuadrados de los catetos es igual
square of the length of the hypotenuse: a2 + b2 = c2. al cuadrado de la hipotenusa: a2 + b2 = c2.

Example 32 ϩ 42 ϭ 52
3 5

Q 4

Quadrants (p. 60)  The four parts into which the Cuadrantes (p. 60)  El plano de coordenadas está dividido
coordinate plane is divided by its axes. por sus ejes en cuatro regiones llamadas cuadrantes.
Quadrant yQuadrant
Example II O I x
Quadrant Quadrant
III IV

Quadratic equation (p. 561)  A quadratic equation is one Ecuación cuadrática (p. 561)  Ecuación que puede
that can be written in the standard form ax2 + bx + c = 0, expresarse de la forma normal como ax2 + bx + c = 0,
where a ≠ 0. en la que a ≠ 0.

Example 4x2 + 9x - 5 = 0

Quadratic formula (p. 582) If ax2 + bx + c = 0 and Fórmula cuadrática (p. 582) Si
2b2 ax2 + bx + c = 0 y a ≠ 0, entonces
a ≠ 0, then x = -b { 2a - 4ac.

x = -b { 2b2 - 4ac.
12 = 0 2a
Example 2x2 + 10x +

x = -b { 2b2 - 4ac
2a

x = - 10 { 2102 - 4(2)(12)
2(2)

x = - 10 { 24
4

x = - 10 + 2 or - 10 - 2
4 4

x = -2 or -3

Quadratic function (p. 546)  A function of the form Función cuadrática (p. 546)  La función
y = ax2 + bx + c, where a ≠ 0. The graph of a quadratic y = ax2 + bx + c, en la que a ≠ 0. La gráfica de una
function is a parabola, a U-shaped curve that opens up función cuadrática es una parábola, o curva en forma de U
or down. que se abre hacia arriba o hacia abajo.

Example y = 5x2 - 2x + 1 is a quadratic
function.

848

English Spanish

Quadratic parent function (p. 546)  The simplest Función cuadrática madre (p. 546)  La función cuadrática
quadratic function f (x) = x2 or y = x2. más simple f (x) = x2 ó y = x2.

Example y = x2 is the parent function for Visual Glossary

the family of quadratic equations
of the form y = ax2 + bx + c.

Qualitative (p. 753)  Data that name qualities are Cualitativo (p. 753)  Los datos que indican cualidades son
qualitative. cualitativos.

Example The data red, blue, red, green,
blue, and blue are qualitative data.

Quantitative (p. 753)  Data that measure quantity and can Cuantitativo (p. 753)  Los datos que miden cantidades y
be described numerically are quantitative. pueden ser descritos numéricamente son cuantitativos.

Example The data 5 ft, 4 ft, 7 ft, 4 ft, 8 ft,
and 10 ft are quantitative.

Quantity (p. 4)  Anything that can be measured Cantidad (p. 4)  Cualquier cosa que se puede medir o
or counted. contar.

Example A dozen is another way to describe
a quantity of 12 eggs.

Quartile (p. 746)  A quartile is a value that separates a Cuartil (p. 746)  Un cuartil es el valor que separa un
finite data set into four equal parts. The second quartile (Q2) conjunto de datos finitos en cuatro partes iguales. El segundo
is the median of the data set. The first and third quartiles cuartil (Q2) es la mediana del conjunto de datos. El primer
(Q1 and Q3) are the medians of the lower half and upper cuartil y el tercer cuartil (Q1 y Q3) son medianas de la mitad
half of the data, respectively. inferior y de la mitad superior de los datos, respectivamente.

Example For the data set 2, 3, 4, 5, 5, 6, 7,
7, the first quartile is 3.5, the
second quartile (or median) is 5,
and the third quartile is 6.5.

R

Radical (p. 16)  An expression made up of a radical symbol Radical (p. 16)  Expresión compuesta por un símbolo radical
and a radicand. y un radicando.

Example 1a

Radical equation (p. 633)  An equation that has a variable Ecuación radical (p. 633)  Ecuación que tiene una variable
in a radicand. en un radicando.

Example 1x - 2 = 12

1x = 14
( 1x)2 = 142
x = 196

Radical expression (p. 619)  Expression that contains Expresión radical (p. 619)  Expresiones que contienen
a radical. radicales.

Example 13, 15x, and 1x - 10 are
examples of radical expressions.

Glossary i 849

English Spanish

Radicand (p. 16)  The expression under the radical sign is Radicando (p. 16)  La expresión que aparece debajo del
the radicand. signo radical es el radicando.

Visual Glossary Example The radicand of the radical
expression 1x + 2 is x + 2.

Range (of a relation or function) (p. 268)  The possible Rango (de una relación o función) (p. 268)  El conjunto
values of the output, or dependent variable, of a relation or de todos los valores posibles de la salida, o variable
function. dependiente, de una relación o función.

Example In the function y = 0 x 0 , the range

is the set of all nonnegative
numbers.

Range of a set of data (p. 740)  The difference between Rango de un conjunto de datos (p. 740)  Diferencia entre
the greatest and the least data values for a set of data. el valor mayor y el menor en un conjunto de datos.

Example For the set 2, 5, 8, 12, the range is
12 - 2 = 10.

Rate (p. 116)  A ratio of a to b where a and b represent Tasa (p. 116)  La relación que existe entre a y b cuando
quantities measured in different units. a y b son cantidades medidas con distintas unidades.

Example Traveling 125 miles in 2 hours
125 miles
results in the rate 2 hours
or 62.5 mi/h.

Rate of change (p. 294)  The relationship between two Tasa de cambio (p. 294)  La relación entre dos cantidades

quantities that are changing. The rate of change is also called que cambian. La tasa de cambio se llama también

slope. change in the dependent variable pendiente. cambio en la variable dependiente
change in the independent variable cambio en la variable independiente
rate of change = tasa de cambio =

Example Video rental for 1 day is $1.99.

Video rental for 2 days is $2.99.

rate of change = 2.99 - 1.99
2 - 1
1.00
= 1

=1

Ratio (p. 116)  A ratio is the comparison of two quantities Razón (p. 116)  Una razón es la comparación de dos
by division. cantidades por medio de una división.

Example 5 and 7 : 3 are ratios.
7

Rational equation (p. 685)  An equation containing Ecuación racional (p. 685)  Ecuación que contiene
rational expressions. expresiones racionales.

Example 1 = 3 1 is a rational equation.
x 2x -

Rational expression (p. 664)  A ratio of two polynomials. Expresión racional (p. 664)  Una razón de dos polinomios.
The value of the variable cannot make the denominator equal El valor de la variable no puede hacer el denominador igual
to 0. a 0.

Example 3 x, where x ≠ 0
x3 +

850

English Spanish

Rational function (p. 699)  A function that can be written Función racional (p. 699)  Función que puede expresarse
de forma f (x) = ppoolliinnoommiioo. El valor de la variable no puede
in the form f (x) = polynomial . The value of the variable cannot hacer el denominador igual a 0.
polynomial
Visual Glossary
make the denominator equal to 0.

Example y = x 2
x2 +

Rationalize the denominator (p. 622)  To rationalize the Racionalizar el denominador (p. 622)  Para racionalizar el

denominator of an expression, rewrite it so there are no denominador de una expresión, ésta se escribe de modo que

radicals in any denominator and no denominators in any no haya radicales en ningún denominador y no haya

radical. denominadores en ningún radical.

#Example 2 = 2 15 = 215 = 215
15 15 15 125 5

Rational number (p. 18)  A real number that can be Número racional (p. 18)  Número real que puede
written as a ratio of two integers. Rational numbers in expresarse como la razón de dos números enteros. Los
decimal form are terminating or repeating. números racionales en forma decimal son exactos o
periódicos.

Example r32a,ti1o.n5a4l8n,uamndbe2r.s2.92929 . . . are all

Real number (p. 18)  A number that is either rational or Número real (p. 18)  Un número que es o racional o
irrational. irracional.

Example 5, - 3, 111, 0re.a6l6n6u.m. b. e, r5s.141, 0,
and p are all

Reciprocal (p. 41)  Given a nonzero bara. tTiohneapl rnoudmucbteor fbaa, the Recíproco (p. 41)  El recíproco, o inverso multiplicativo, de
reciprocal, or multiplicative inverse, is unnúmnúermoerraociqounealnbao cuyo valor no es cero es ba. El producto
un es cero y su valor recíproco es 1.
nonzero number and its reciprocal is 1. de

Example 2 and 5 are reciprocals because
5 2

2 * 5 = 1.
5 2

Recursive formula (p. 275)  A recursive formula defines Fórmula recursiva (p. 275)  Una fórmula recursiva define
the terms in a sequence by relating each term to the ones los términos de una secuencia al relacionar cada término con
before it. los términos que lo anteceden.

Example Let an = 2.5an-1 + 3an-2.

If a5 = 3 and a4 = 7.5, then
a6 = 2.5(3) + 3(7.5) = 30.

Relation (p. 268)  Any set of ordered pairs. Relación (p. 268)  Cualquier conjunto de pares ordenados.

Example {(0, 0), (2, 3), (2, -7)} is a relation.

Glossary i 851

English Spanish

Visual Glossary Relative error (p. 146)  The ratio of the absolute value of Error relativo (p. 146)  Razón del valor absoluto de la
the difference of a measured (or estimated) value and an diferencia de un valor medido (o estimado) y un valor actual
actual value compared to the actual value. en comparación con el valor actual.

Example You estimated that a plant would

be 5 in. tall 3 months after it was

planted. The plant was actually

5.5 in. tall 3 months after it was

planted. The relative error is

05 - 5.5 0 = 0 - 0.5 0 = 0.5 = 1 ,
5.5 5.5 5.5 11

or about 9%.

Residual (p. 344)  The difference between the y-value of a Residuo (p. 344)  La diferencia entre el valor de y de un
data point and the corresponding y-value of a model for the punto y el valor de y correspondiente a ese punto en el
data set. modelo del conjunto de datos.

Root of the equation (p. 561)  A solution of an equation. Ráiz de la ecuación (p. 561)  Solucion de una ecuación.

Roster form (p. 194)  A notation for listing all of the Lísta (p. 194)  Una notación en la que se enlistan todos los
elements in a set using set braces and commas. elementos en un conjunto usando llaves y commas.

Example The set of prime numbers less than
10, expressed in roster form, is
{2, 3, 5, 7}.

S

Sample (p. 754)  The part of a population that is surveyed. Muestra (p. 754)  Porción que se estudia de una población.

Example Let the set of all males between
the ages of 19 and 34 be the
population. A random selection of
900 males between those ages
would be a sample of the
population.

Sample space (p. 769)  All possible outcomes in a Espacio muestral (p. 769)  Todos los resultados posibles de
situation. una ecuación.

Example When you roll a number cube, the
sample space is {1, 2, 3, 4, 5, 6}.

Scalar (p. 727)  A real number is called a scalar for certain Escalar (p. 727)  Un número real se llama escalar en ciertos
special uses, such as multiplying a matrix. See Scalar casos especiales, como en la multiplicación de una matriz. Ver
multiplication. Scalar multiplication.

Example 2.5 J - 1 0 = 2.5(1) 2.5(0)
2 3R J2.5(- 2) 2.5(3) R

       = 2.5 0
J -5 7.5 R

852

English Spanish

Scalar multiplication (p. 727)  Scalar multiplication is an Multiplicación escalar (p. 727)  La multiplicación escalar es Visual Glossary
operation that multiplies a matrix A by a scalar c. To find the la que multiplica una matriz A por un número escalar c. Para
resulting matrix cA, multiply each element of A by c. hallar la matriz resultante cA, multiplica cada elemento de
A por c.

Example 2.5 J - 1 0 = 2.5(1) 2.5(0)
2 3R J2.5(- 2) 2.5(3) R

       = 2.5 0
J -5 7.5 R

Scale (p. 132)  The ratio of any length in a scale drawing Escala (p. 132) Razón de cualquier longitud de un dibujo a
to the corresponding actual length. The lengths may be in escala a la longitud real correspondiente. Las longitudes
different units. pueden tener diferentes unidades.

Example For a drawing in which a
2-in. length represents an actual
length of 18 ft, the scale is
1 in. : 9 ft.

Scale drawing (p. 132)  An enlarged or reduced drawing Dibujo a escala (p. 132)  Dibujo que muestra de mayor o
similar to an actual object or place. menor tamaño un objeto o lugar dado.

Example

1 in.

3 in. Kitchen
4

1 in. 121 in.
4

1 in. Dining Room
4

121 in.

Scale model (p. 132)  A three-dimensional model that is Modelo de escala (p. 132)  Modelo tridimensional que es
similar to a three-dimensional object. similar a un objeto tridimensional.

Example A ship in a bottle is a scale model
of a real ship.

Glossary i 853

English Spanish

Scatter plot (p. 336)  A graph that relates two different sets Diagrama de puntos (p. 336)  Gráfica que muestra la
of data by displaying them as ordered pairs. relación entre dos conjuntos. Los datos de ambos conjuntos
se presentan como pares ordenados.
Visual Glossary
Sales (millionsExample 40 Sales vs. Advertising
of dollars) 30
20
10
00 10 20 30 40 50
Advertising (thousands of dollars)

The scatter plot displays the amount spent
on advertising (in thousands of dollars)
versus product sales (in millions of dollars).

Scientific notation (p. 427)  A number expressed in the Notación científica (p. 427)  Un número expresado en
forma de a * 10n, donde n es un número entero y
form a * 10n, where n is an integer and 1 6 0 a 0 6 10.
1 6 0 a 0 6 10.
Example 3.4 * 106

Sequence (p. 274)  An ordered list of numbers that often Progresión (p. 274)  Lista ordenada de números que
forms a pattern. muchas veces forma un patrón.

Example -4, 5, 14, 23 is a sequence.

Set (p. 17)  A well-defined collection of elements. Conjunto (p. 17)  Un grupo bien definido de elementos.

Example The set of integers:
Z = 5. . . , -3, -2, -1, 0, 1, 2, 3, . . .6

Set-builder notation (p. 194)  A notation used to describe Notación conjuntista (p. 194)  Notación que se usa para
the elements of a set. describir los elementos de un conjunto.

Example The set of all positive real numbers

in set-builder notation is 5x 0 x ∈ ℝ
and x 7 06. This is read as “the set

of all values of x such that x is a real
number and x is greater than 0.”

Similar figures (p. 130)  Similar figures are two figures that Figuras semejantes (p. 130)  Dos figuras semejantes son
have the same shape, but not necessarily the same size. dos figuras que tienen la misma forma pero no son
necesariamente del mismo tamaño.
Example D
G

E
FH

I
△DEF and △GHI are similar.

854

English Spanish

Simple interest (p. 139)  Interest paid only on the principal. Interés simple (p. 139)  Intéres basado en el capital
solamente.

Example The interest on $1000 at 6% for Visual Glossary
5 years is $1000(0.06)5 = $300.

Simplify (p. 10)  To replace an expression with its simplest Simplificar (p. 10)  Reemplazar una expresión por su
name or form. versión o forma más simple.

Example (3)+ 5*
8

Sine (p. 645)  In a right triangle, such as △ABC, with Seno (p. 645)  En un triángulo rectángulo tal que △ABC
right ∠C, con ∠C recto,

sine of ∠A = length of side opposite ∠ A or sin A = ac. el seno de ∠A = longitud del lado opuesto a ∠ A , o sen A = ac.
length of hypotenuse longitud de la hipotenusa

Example A sin A ‫؍‬ 4
5 5

3

C 4B

Slope (p. 295)  The ratio of the vertical change to the Pendiente (p. 295)  La razón del cambio vertical al cambio

horizontal change. horizontal.

slope = vertical change = y2 - y1 , where x2 - x1 ≠ 0 pendiente = cambio vertical = y2 - yx11, donde x2 - x1 ≠ 0
horizontal change x2 - x1 cambio horizontal x2 -

Example 2 y (4, 2)
4x
O2

The slope of the line above is 2 ϭ 1 .
4 2

Slope-intercept form (p. 308)  The slope-intercept form of Forma pendiente-intercepto (p. 308)  La forma
a linear equation is y = mx + b, where m is the slope of the pendiente-intercepto es la ecuación lineal y = mx + b, en la
line and b is the y-intercept. que m es la pendiente de la recta y b es el punto de

Example y = 8x - 2 intersección de esa recta con el eje y.

Solution of an equation (one variable) (p. 54)  Any value Solución de una ecuación (una variable) (p. 54) 
or values that make an equation true. Cualquier valor o valores que hagan verdadera una ecuación.

Example 3 is the solution of the equation
4x - 1 = 11.

Solution of an equation (two variables) (p. 61)  Solución de una ecuación (dos variables) (p. 61) La
A solution of a two-variable equation with the variables solución de una ecuación con dos variables que tiene las
x and y is any ordered pair (x, y) that makes the equation variables x e y es cualquier par ordenado que hace que la
true. ecuación sea verdadera.

Example (4, 1) is one solution of the
equation x = 4y.

Glossary i 855

English Spanish

Visual Glossary Solution of an inequality (one variable) (p.165)  Solución de una desigualdad (una variable) (p. 165) 
Any value or values of a variable in the inequality that makes Cualquier valor o valores de una variable de la desigualdad
an inequality true. que hagan verdadera la desigualdad.

Example The solution of the inequality
x 6 9 is all numbers less than 9.

Solution of an inequality (two variables) (p. 394)  Solución de una desigualdad (dos variables) (p. 394) 
Any ordered pair that makes the inequality true. Cualquier par ordenado que haga verdadera la desigualdad.

Example EEacahchorodredreedrepdaipr ainirthine tyheleloywellow
aareraeaanadndonotnhtehseolsidolrieddrleindeliisnae
siosluatisoonluotfio3nx -of53yx…Ϫ105.y Յ 10.

2y


Ϫ2 O 2 4 6 8 x

Solution of a system of linear equations (p. 364)  Solución de un sistema de ecuaciones lineales (p. 364) 
Any ordered pair in a system that makes all the equations Todo par ordenado de un sistema que hace verdaderas todas
of that system true. las ecuaciones de ese sistema.

Example (2, 1) is a solution of the system

y = 2x - 3
y=x-1
because the ordered pair makes
both equations true.

Solution of a system of linear inequalities (p. 400)  Solución de un sistema de desigualdades lineales (p. 400) 
Any ordered pair that makes all of the inequalities in the Todo par ordenado que hace verdaderas todas las
system true. desigualdades del sistema.

Example 4y

2 x
246
Ϫ2 O
Ϫ2

Ϫ4

Theeshshadaeddedgrgeereneanreaarsehaoswhsotwhes the
ssoolulutiotinonofotfhtehseysstyesmte3myx 7+3xy42yϩxϾ6-4251yx2ϽϪ. 5
12.

856

English Spanish

Square root (p. 16)  A number a such that a2 = b. 1b is Raíz cuadrada (p. 16) Si a2 = b, entonces a es la raíz
the principal square root. - 1b is the negative square root. cuadrada de b. 1b es la raíz cuadrada principal. - 1b es la
raíz cuadrada negativa.
Visual Glossary
Example -3 and 3 are square roots of 9.

Square root function (p. 642)  A function that contains Función de raíz cuadrada (p. 642)  Una función que
the independent variable in the radicand. contiene la variable independiente en el radicando.

Example y = 12x is a square root function.

Standard deviation (p. 745)  A measure of how data Desviación típica (p. 745)  Medida de cómo los datos
varies, or deviates, from the mean. varían, o se desvían, de la media.

Example Use the following formula to find

the standard deviation.

= a (x - x)2
n
s 7

Standard form of a linear equation (p. 322) The Forma normal de una ecuación lineal (p. 322)  La forma
standard form of a linear equation is Ax + By = C , where normal de una ecuación lineal es Ax + By = C , donde A, B
A, B, and C are real numbers and A and B are not both zero. y C son números reales, y donde A y B no son iguales a cero.

Example 6x - y = 12

Standard form of a polynomial (p. 487)  The form of a Forma normal de un polinomio (p. 487)  Cuando el grado
polynomial that places the terms in descending order de los términos de un polinomio disminuye de izquierda a
by degree. derecha, está en forma normal, o en orden descendente.

Example 15x3 + x2 + 3x + 9

Standard form of a quadratic equation (p. 561) The Forma normal de una ecuación cuadrática (p. 561) 
standard form of a quadratic equation is ax2 + bx + c = 0, Cuando una ecuación cuadrática se expresa de forma
where a ≠ 0. ax2 + bx + c = 0.

Example - x2 + 2x - 9 = 0

Standard form of a quadratic function (p. 546) The Forma normal de una función cuadrática (p. 546) 
standard form of a quadratic function is f(x) = ax2 + bx + c, La forma normal de una función cuadrática es
where a ≠ 0. f(x) = ax2 + bx + c, donde a ≠ 0.

Example f(x) = 2x2 - 5x + 2

Stem-and-leaf plot (p. 734)  A display of data made by Diagrama de tallo y hojas (p. 734)  Un arreglo de los
using the digits of the values. datos que usa los dígitos de los valores.

Example Number of Points

0 17
1 002
2 33778
3 21599

Key: 2 ͉ 3 means 23

Glossary i 857

English Spanish

Visual Glossary Step function (p. 348)  A step function pairs every number Función escalón (p. 348)  Una función escalón empareja
in an interval with a single value. The graph of a step cada número de un intervalo con un solo valor. La gráfica de
function can look like the steps of a staircase. una función escalón se puede parecer a los peldaños de una
escalera.

Subset (p.17)  A subset of a set consists of elements from Subconjunto (p. 17)  Un subconjunto de un conjunto
the given set. consiste en elementos del conjunto dado.

Example If B = 51, 2, 3, 4, 5, 6, 76
and A = 51, 2, 56, then A is a
subset of B.

Substitution method (p. 372)  A method of solving a Método de sustitución (p. 372)  Método para resolver un
system of equations by replacing one variable with an sistema de ecuaciones en el que se reemplaza una variable
equivalent expression containing the other variable. por una expresión equivalente que contenga la otra variable.

Example If y = 2x + 5 and
x + 3y = 7, then
x + 3(2x + 5) = 7.

System of linear equations (p. 364)  Two or more linear Sistema de ecuaciones lineales (p. 364)  Dos o más
equations using the same variables. ecuaciones lineales que usen las mismas variables.

Example y = 5x + 7

y = 1 x - 3
2

System of linear inequalities (p. 400)  Two or more linear Sistema de desigualdades lineales (p. 400)  Dos o más
inequalities using the same variables. desigualdades lineales que usen las mismas variables.

Example y … x + 11
y 6 5x

T

Tangent (p. 645)  In a right triangle, such as △ABC with Tangente (p. 645)  En un triángulo rectángulo tal que
right ∠C , △ABC, con ∠C recto,
length of side opposite ∠ A ba. longitud del lado opuesto a ∠ A
tangent of ∠A = length of side adjacent to ∠ A , or tan A = la tangente de ∠ A = longitud del lado adyacente a ∠ A ,
o la tan A = ba.

Example A tan A ‫؍‬ 4
3 5 3

C 4B

Term (p. 48)  A number, variable, or the product or quotient Término (p. 48)  Un número, una variable o el producto o
of a number and one or more variables. cociente de un número y una o más variables.

Example The expression 5x + y - 8 has
three terms: 5x, 2y, 2
and -8.

Term of a sequence (p. 274)  A term of a sequence is any Término de una progresión (p. 274)  Un término de una
number in a sequence. secuencia es cualquier número de una secuencia.

Example -4 is the first term of the
sequence -4, 5, 14, 23.

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English Spanish

Theoretical probability (p. 769)  The ratio of the number Probabilidad teórica (p. 769)  Si cada resultado tiene la Visual Glossary
of favorable outcomes to the number of possible outcomes if misma probabilidad de darse, la probabilidad teórica de un
all outcomes have the same chance of happening. suceso se calcula como la razón del número de resultados
favorables al número de resultados posibles.
number of favorable outcomes
P(event) = number of possible outcomes P(suceso) = numero de resultados favorables
numero de resultados posibles

Example In tossing a coin, the events of
getting heads or tails are equally
likely. The likelihood of getting
heads is P(heads) = 21.

Translation (p. 346)  A transformation that shifts a graph Translación (p. 346)  Proceso de mover una gráfica
horizontally, vertically, or both. horizontalmente, verticalmente o en ambos sentidos.

Example y ‫ͦ ؍‬xͦ y

y ‫؍‬ ͦxϪ؉2 O x
2Ϫͦ 2 24

y ϭ ͉x ϩ 2͉ is a translation
of y ϭ ͉x͉.

Trend line (p. 337)  A line on a scatter plot drawn near the Línea de tendencia (p. 337)  Línea de un diagrama de
points. It shows a correlation. puntos que se traza cerca de los puntos para mostrar una
correlación.
Example

Positive Negative

Trigonometric ratios (p. 645)  The ratios of the sides of a Razones trigonométricas (p. 645)  Las razones de los
right triangle. See cosine, sine, and tangent. lados de un triángulo rectángulo. Ver coseno, seno, y
tangente.

Trinomial (p. 487)  A polynomial of three terms. Trinomio (p. 487)  Polinomio compuesto de tres términos.

Example 3x2 + 2x - 5

U

Union (p. 214)  The set that contains all of the elements of Unión (p. 214)  El conjunto que contiene todos los
two or more sets. elementos de dos o más conjuntos.

Example If A = 51, 3, 6, 96 and

B = 51, 5, 106, then the union
of A and B, or A ∪ B, is
51, 3, 5, 6, 9, 106.

Glossary i 859

English Spanish

Unit analysis (p. 117)  Including units for each quantity in Análisis de unidades (p. 117)  Incluir unidades para cada
a calculation to determine the unit of the answer. cantidad de un cálculo como ayuda para determinar la
unidad que se debe usar para la respuesta.
Visual Glossary
Example To change 10 ft to yards,
multiply by the conversion

factor 1 yfdt .
3

( )10 ft 1 yd = 3 1 yd
3 ft 3

Unit rate (p. 117)  A rate with a denominator of 1. Razón en unidades (p. 117)  Razón cuyo denominador es 1.

Example The unit rate for 120 miles driven
in 2 hours is 60 mi/h.

Univariate (p. 754)  A set of data that uses only one Univariado (p. 754)  Un conjunto de datos que tiene sólo
variable is univariate. una variable es univariado.

Universal set (p. 196)  The set of all possible elements Conjunto universal (p. 196)  Conjunto de todos los
from which subsets are formed. posibles elementos específicos del cual se forma un
subconjunto.

Unlike radicals (p. 626)  Radical expressions that do not Radicales no semejantes (p. 626)  Expresiones radicales
have the same radicands. que no tienen radicandos semejantes.

Example 12 and 13 are unlike radicals.

V

Variable (p. 4)  A symbol, usually a letter, that represents Variable (p. 4)  Símbolo, generalmente una letra, que
one or more numbers. representa uno o más valores de una cantidad.

Example x is the variable in the equation
9 - x = 3.

Vertex (p. 547)  The highest or lowest point on a parabola. Vértice (p. 547)  El punto más alto o más bajo de una
The axis of symmetry intersects the parabola at the vertex. parábola. El punto de intersección del eje de simetría y la
parábola.

Example y

1x
O2
vertex

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