Chapter  3.4 Transformation of Graphs

Pindling College Algebra   by Example  Series

Key Concepts: Understand how graphs can be transformed from their original equations or graphs

Skills to Learn

1. Know how to perform the following transformation on a graph or its function

(a) Vertical Translations

(b) Horizontal Translations

(c) Reflection about the y-axis

(d) Reflection about the x-axis

(e) Vertical Stretches

(f) Horizontal Stretches

Recommended order of transformation: (1) Horizontal Translation, (2) Horizontal Stretch (3) Horizontal Reflection (4)
Vertical Reflection (5) Vertical Stretch, (5) Vertical Translation

Summary of Transformations:

Vertical and Horizontal Translations

Transformation	On f(x)	By Example:	Illustration for
Horizontal Translation When h is +, shift Right When h is (-), shift Left		Shift Right Shift Left
Vertical Translation When k is +, shift Up When k is (-), shift Down		Shift Up Shift Down

Reflections about the y- and x-axes

Transformation	On f(x)	By Example: and	Illustration for
Reflection about the y-axis Reflection when		Reflection about y-axis If then Is a reflection about the y-axis
Reflection about the x-axis Reflection when		Reflection about x-axis If then Is a reflection about the x-axis

Vertical and Horizontal Stretches

Transformation	On f(x)	By Example:	Illustration for
Vertical Stretches When A is >1, graph Expands When A is < 1, graph Contracts		for Vertical Expansion if Vertical Contraction if
Horizontal Stretches When B is >1, graphs Contracts When B is < 1, graph Expands		for Horizontal Compression if (B = 2) Horizontal Expansion if (B = ½ )

Transformation by Examples

Horizontal Translations

Example 7	Example 8
Example 9	Example 10

Vertical Translations

Example 11	Example 12
Example 13	Example 14

Reflection about the y-axis

Example 15	Example 16
Example 17	Example 18

Reflection about the x-axis

Example 19	Example 20
Example 21	Example 22

Horizontal Stretch

Example 23	Example 24
Example 25	Example 26

Vertical Stretch

Example 27	Example 28
Example 29	Example 30

Combined Transformation

Given Graph of Sketch