Section 2.7 – A Preview of Transformations

• Objective:– Identify the transformation(s) from

one function to another

• Standard:– 2.8.11.Q. Represent functional

relationships in tables, charts, and graphs

Parent Functions• Quadratic Function

f(x) = x2

• Absolute Value Function

f(x) = lxl

• Radical Function

f(x) = √x

Vertical Translations• Consider the Quadratic parent function

– How can we move this graph 2 spaces up?

– How about 4 spaces down?

Horizontal Translations • Consider the Absolute Value parent

function • How can we move this graph 3 spaces

to the left?

• How about 5 spaces to the right?

Vertical Stretch and Compression

• Consider the Radical parent function• How can we vertically stretch this graph

by a factor of 4?

How can we vertically compress this graph How can we vertically compress this graph by a factor of ½ ?by a factor of ½ ?

Horizontal Stretch and Compression

• Lets consider the Quadratic parent function.• How can we horizontally stretch this graph by a

factor of 4?

• How can we horizontally compress this graph by a factor of ⅓?

Reflections• Let’s consider the Radical parent function• How can we Vertically Reflect (across the x-

axis) this graph?

• How can we Horizontally Reflect (across the y-axis) this graph?

Combined Transformations

1. xxg 4)( Horizontal Reflection & Horizontal Compression by a factor of ¼

2. 34)( xxg Vertical Reflection, Horizontal Translation 4, & Vertical Translation 3

Identify each transformation from the parent function xxf )(

Write the function for each graph described.

3. The graph of vertically stretched by a factor of 2 and translated 1 unit to the right.

2)( xxf 2)1(2)( xxg

4. The graph of reflected across the x-axis, stretched horizontally by a factor of 5 and translated up 4

xxf )(

45

1)( xxh

Summary

Homework

Integrated Algebra II- Section 2.7 Level A

Honors Algebra II- Section 2.7 Level B