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Transformation of Functions using a Graphing Calculator

Module by: Debbie Trahan

Summary: The objective of this module is for students to explore the transformations of functions using a graphing calculator.

Transformations of Functions with a Graphing Calculator

In this lesson you will investigate transformations of functions using a graphing calculator.

Transformations with a Quadratic Function

Use a standard window as shown in figure 1, to graph the function fx=x2 f x x 2 using a graphing calculator. (figure 2)

Figure 1
Figure 1 (qwin.png)
Figure 2
Figure 2 (qprob.png)

Example 1

In problems 1 - 3, you will be given a calculator screen with the function fx f x graphed using a broken curve and a transformation of fx f x graphed using a solid curve. see figure 3

Figure 3
Figure 3 (qprob1.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Answer a: y=x2-5 y x 2 5

Part b: Use function notation to represent this transformation.

Answer b: fx-5 f x 5

Exercise 1

In figure 4, the graph of fx f x is a broken curve and the graph of the transformation is a solid curve.

Figure 4
Figure 4 (qprob2.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 1

Part a: y=x+32 y x 3 2

Part b: fx+3 f x 3

Exercise 2

In figure 5, the graph of fx f x is a broken curve and the graph of the transformation is a solid curve.

Figure 5
Figure 5 (qprob3.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 2

Part a. y=-x2 y x 2

Part b. -fx f x

Exercise 3

In figure 6, the graph of fx f x is a broken curve and the graph of the transformation is a solid curve.

Figure 6
Figure 6 (qprob4.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 3

Part a. y=.5x2 y .5 x 2

Part b. .5fx .5 f x

Transformations with a Cubic Function

Use a standard window as shown in figure 1, to graph the function fx=x3-x2-6x f x x 3 x 2 6 x using a graphing calculator. (figure 7)

Figure 7
Figure 7 (cprob.png)

Exercise 4

In figure 8, the graph of fx=x3-x2-6x f x x 3 x 2 6 x is a broken curve and the graph of the transformation is a solid curve.

Figure 8
Figure 8 (cprob1.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 4

fx=x-43-x-42-6x-4 f x x 4 3 x 4 2 6 x 4

Exercise 5

In figure 9, the graph of fx=x3-x2-6x f x x 3 x 2 6 x is a broken curve and the graph of the transformation is a solid curve.

Figure 9
Figure 9 (cprob2.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 5

fx=x3+x2-6x+5 f x x 3 x 2 6 x 5

Exercise 6

In figure 10, the graph of fx=x3-x2-6x f x x 3 x 2 6 x is a broken curve and the graph of the transformation is a solid curve.

Figure 10
Figure 10 (cprob3.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 6

fx=-x3--x2-6-x f x x 3 x 2 6 x

Exercise 7

In figure 11, the graph of fx=x3-x2-6x f x x 3 x 2 6 x is a broken curve and the graph of the transformation is a solid curve.

Figure 11
Figure 11 (cprob4.png)

Part a: Write the equation that will produce the transformation then use a calculator to check your answer.

Part b: Use function notation to represent this transformation.

Solution 7

fx=-x3+x2-6x f x x 3 x 2 6 x

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 (Graphically) Module

Go to Transformation of Functions (Verbally) Module

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