BUC Beginning
What does the word “transformation” mean?
Today you need:
2 pieces of graph paper into 8 pieces
scissors
glue
2 colors
Transformations to Parent
Functions
Translation (Shift)
A vertical translation is made on a function
by adding or subtracting a number to the
function.
Example: y = x + 3 (translation up)
Example: y = x² - 5 (translation down)
A translation up is also called a vertical shift
up.
A translation down is also called a vertical
shift down.
Example: y = |x| + 2
Parent function (y = |x|)
The transformation
of the parent
function is shown in
blue. It is a shift up
(or vertical
translation up) of 2
units.
Example: y = x - 1
Parent function (y = x)
The transformation
of the parent
function is shown in
blue. It is a shift
down (or vertical
translation down) of
1 unit.
BUC Beginning
What does it mean to reflect an image OVER the
x-axis?
Reflection
A reflection on the x-axis is made on a
function by multiplying the parent function
by a negative.
Multiplying by a negative “flips” the graph of
the function over the x-axis.
Example: y = -x² is a reflection of the parent
function y = x².
Example: y = - x²
The reflection of
the parent
function is shown
in blue. It is a
reflection over the
x-axis of the
function y = x²
Stretch
A stretch is made on a parent function by
multiplying the parent function by a number
x such that
|x| > 1.
Example: y = 3x²
A stretch is also referred to as a narrowing of
the graph of the function closer to the y-axis.
Example: y = 2x
The blue line
shows the
graph of the
stretch of the
parent
function,
y = 2x, by a
scale factor of
2.
Shrink
A shrink is made on a function by multiplying
the parent function by a number x such that
0 < |x| < 1.
Example: y = (½) x.
A shrink is also referred to as a widening of
the graph of the function closer to the x-axis.
Example: y = (¼) x
The blue line
shows the graph
of the shrink of
the parent
function, y =
(¼)x, by a scale
factor of ¼.
What happens when we combine the two (blue is parent function)?
y (x 6)2 2