CH 5 L2 (MADAM MAI)

- CHAPTER 5

FUNCTIONS
& GRAPHS

LECTURE 2 OF 9

Learning Outcomes

01 Sketching Graph
Surd and absolute value
function

02 Domain & Range

Surd and absolute value
function

Basic Graph STEPS TO SKETCH SURD FUNCTION GRAPH
1. Find domain
iv) Surd Function 2. Find 2 points in domain
3. Sketch curve that passes through the
= +
points
f(x)
= = − +

f(x)

0x

x = −
0

: [0, ∞) : [0, ∞)
: [0, ∞) : (−∞, 0]

Domain & Range from Graph

Surd Function

f(x) f(x) x
(2, 3) 0
x
(−3, −1)
0

: [2, ∞)
: [3, ∞) : [−3, ∞)
: (−∞, −1]

Example 1

Find the domain and range for = 2 + − 1 and sketch its graph

1st Find domain 2nd Find 2 points 3rd Sketch curve
in domain
f(x)

3x x
x2

(1, 2)

12

: [1, ∞)
: [2, ∞)

Example 2

Find the domain and range for = 3 − 2 − and sketch its graph

1st Find domain 2nd Find 2 points 3rd Sketch curve
in domain

f(x)

x(2, 3)

3

1.586

x x−7 2 x

: (−∞, 2]
: (−∞, 3]

Domain & Range using Algebraic Approach

Surd Function
Find the domain and range for
Find the domain and range for

= 2 + − 1 = 3 − 1 −

: [1, ∞) : (−∞, 1]
: [2, ∞) : (−∞, 3]

Basic Graph STEPS TO SKETCH ABSOLUTE VALUE
FUNCTION GRAPH
v) Absolute Value Function
1. Find vertex point
2. Find 2 points before and after vertex

point
3. Sketch V-Shape line that passes

through the points

= | + | f(x) = −| + |
0
f(x) x
= | |

= −| |

x
0

: (−∞, ∞) : (−∞, ∞)
: [0, ∞) : (−∞, 0]

Domain & Range from Graph

Absolute Value Function

f(x) f(x) x
0

(3,4) (2, −6)
x

0

: (−∞, ∞) : (−∞, ∞)
: [4, ∞) : (−∞, −6]

Example 3

Sketch the graph of ( ) = 2 − 1 − 2. Find its domain and range

1st Find vertex 2nd Find 2 points before 3rd Sketch V-shape line
point and after vertex
point f(x)

0.5 x x

x-0.5 -1 1.5
x x-2
(0.5, −2)

: (−∞, ∞)
: [−2, ∞)

Example 4

Sketch the graph of ( ) = 5 − + 1 . Find its domain and range

1st Find vertex 2nd Find 2 points before 3rd Sketch V-shape line
point and after vertex
point f(x)

(−1, 5) 5 x
4
x x x x-6 -1
4

: (−∞, ∞)
: (−∞, 5]

Domain & Range using Algebraic Approach

Absolute Value Function

Find the domain and range for Find the domain and range for
= − 5 − 2 = 5 − − 2

: (−∞, ∞) : (−∞, ∞)
: [−2, ∞) : (−∞, 5]