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# Transformation of Functions (Graphically)

Module by: Debbie Trahan. E-mail the author

Summary: In this module students will apply transformations to the graph of a function.

The objective of this module is to apply tranformations to the graph of a function.

The graph of the function hx h x is shown in figure 1 . Transfer this graph to your paper. Use the graph of hx h x to help you answer parts a and b for each of the problems 1 - 8.

a. Explain how the given transformation will change the graph of hx h x .

b. Graph the transformation.

## Exercise 1

Answer parts a and b for the given transformation. hx2 h x 2

### Solution

The transformation will translate the graph of hx h x 2 units to the right. (figure 2)

## Exercise 2

Answer parts a and b for the given transformation. hx3 h x 3

### Solution

The transformation will translate the graph of hx h x 3 units down. (figure 3)

## Exercise 3

Answer parts a and b for the given transformation. hx h x

### Solution

The transformation will reflect the graph of hx h x over the x - axis. (figure 4)

## Exercise 4

Answer parts a and b for the given transformation. hx h x

### Solution

The transformation reflect the graph of hx h x over the y - axis. (figure 5)

## Exercise 5

Answer parts a and b for the given transformation. 2hx 2 h x

### Solution

The transformation will vertically stretch the graph of hx h x by a scale factor of 2. (figure 6)

## Exercise 6

Answer parts a and b for the given transformation. 12hx 1 2 h x

### Solution

The transformation will vertically compress the graph of hx h x by a scale factor of 12 1 2 . (figure 7)

## Exercise 7

Answer parts a and b for the given transformation. h2x h 2 x

### Solution

The transformation will horizontally compress the graph of hx h x by a scale factor of 12 1 2 . (figure 8)

## Exercise 8

Answer parts a and b for the given transformation. h13x h 1 3 x

### Solution

The transformation will horizontally stretch the graph of hx h x by a scale factor of 3. (figure 9)

## Transformations of Functions Exploration Modules

After you have completed this lesson you can continue to explore transformations of functions by choosing a module listed below.

Go to Transformation of Functions Exploration Module

Go to Transformation of Functions using a Graphing Calculator Module

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