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Transformation of Functions (Graphically)

Module by: Debbie Trahan

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

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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.

Figure 1
Figure 1 (hprob.gif)

Exercise 1

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

Solution

The transformation will translate the graph of hx 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. hx−3 h x 3

Solution

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

Figure 3
Figure 3 (hansb.gif)

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)

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 hx 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. 2hx 2 h x

Solution

The transformation will vertically stretch the graph of hx 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. 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)

Figure 7
Figure 7 (hansf.gif)

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)

Figure 8
Figure 8 (hansg.gif)

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)

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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