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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 h⁢x h x is shown in figure 1 . Transfer this graph to your paper. Use the graph of h⁢x 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 h⁢x h x .

b. Graph the transformation.

Figure 1
Figure 1 (hprob.gif)

Exercise 1

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

Solution

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

Figure 2
Figure 2 (hansa.gif)

Exercise 2

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

Solution

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

Figure 3
Figure 3 (hansb.gif)

Exercise 3

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

Solution

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

Figure 4
Figure 4 (hansc.gif)

Exercise 4

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

Solution

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

Figure 5
Figure 5 (hansd.gif)

Exercise 5

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

Solution

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

Figure 6
Figure 6 (hanse.gif)

Exercise 6

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

Solution

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

Figure 7
Figure 7 (hansf.gif)

Exercise 7

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

Solution

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

Figure 8
Figure 8 (hansg.gif)

Exercise 8

Answer parts a and b for the given transformation. h⁢13⁢x h 1 3 x

Solution

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

Figure 9
Figure 9 (hansh.gif)

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 (Verbally) Module

Go to Transformation of Functions using a Graphing Calculator Module

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