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Published by tlgardne, 2017-10-09 12:05:22

Function Transformations

Function Transformations

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


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