Function Transformations Discovery Worksheet

Directions

This worksheet will show you various types of function transformations, and allow you to discover the effect of each transformation on the original graph of the function shown in green. Use the slider, or click the play button in the left column to change the value of a. This will create four different types of transformations shown below the slider, and shown in the graphing window. You can hide any of these transformations by clicking on the colored button to the left of the function rules. Investigate the patterns that occur when transforming functions, and answer the questions below.

1.

What happens when you add to the input f(x+a) shown with the red graph?

2.

What happens when you add to the output f(x)+a shown with the blue graph?

3.

What happens when you multiply the input f(a*x) shown with the orange graph?

4.

What happens when you multiply the output a*f(x) shown with the purple graph?

5.

Change the function to . Are your answers to questions 1-4 the same? What is different than your predictions from questions 1-4?

6.

Change the funciton to . Are your answers to questions 1-5 the same? What is different than your predictions from questions 1-5?

7.

What can you conclude about the effects of the following? -Adding to the input f(x+a) -Adding to the output f(x)+a -Multiplying the input f(a*x) -Multiplying the output a*f(x)

8. What is true in general about a change to a functions input?

Tick all that apply

A
It affects the graph horizontally in the "opposite" direction
B
It affects the graph vertically in the "opposite" direction
C
It affects the graph horizontally in the "anticipated" direction
D
It affects the graph vertically in the "anticipated" direction

Check my answer (3)

9.

What is true in general about a change to a functions output?

Tick all that apply

A
It affects the graph horizontally in the "opposite" direction
B
It affects the graph vertically in the "opposite" direction
C
It affects the graph horizontally in the "anticipated" direction
D
It affects the graph vertically in the "anticipated" direction

Check my answer (3)

10.

What is true about an additive change to a function?

Tick all that apply

A
It shifts the graph
B
It stretches/compresses the graph

Check my answer (3)

11.

What is true about a multiplicative change to a function?

Tick all that apply

A
It shifts the graph
B
It stretches/compresses the graph

Check my answer (3)

Function Transformations Discovery Worksheet

Directions

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8. What is true in general about a change to a functions input?

9.

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