Module 1: Function Transformations

 

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tip
This lesson focuses on combining the transformations you have learned so far. You may find it useful to keep a summary of transformations handy.

In Try This 1 you saw that it was possible to perform stretches, reflections, and translations across the same function. When multiple transformations are used, the order in which they are applied is significant. Complete the following investigation to see how important order is.

 

This picture shows the reflection of a building in an office tower.

Hemera/Thinkstock

 

Try This 2


textbook

Complete “Investigate the Order of Transformations” questions 1 to 7 on pages 32 and 33 of the textbook. A table similar to the following, which includes examples of transformations from some of the questions, may help you organize the information. Working on graph paper will be helpful for this exercise.

 

 

Transformation

Sketch

How do the two transformations compare?

Does order matter?
Stretches 1.b. vertical stretch, then horizontal stretch

 

 

 

1.c. horizontal stretch, then vertical stretch

 
Vertical Reflection and Translation

3.b. reflection across the x-axis, then vertical translation

 

 

 

3.c. vertical translation, then reflection across the x-axis

 

Horizontal Reflection and Translation

5.b. reflection across the y-axis, then horizontal translation

 

 

 

5.c. horizontal translation, then reflection across the y-axis

 
Vertical Stretch and Translation

7.a. vertical stretch, then vertical translation

 

 

 

7.a. vertical translation, then vertical stretch

 

 

course folder Save your responses in your course folder.

 

Share 2

 

With a partner or group, discuss the following questions based on the table you created in Try This 2.

  1. Is the order of stretching and reflecting important? Explain.
  2. Is the order of a horizontal translation and a reflection across the x-axis important? Explain.
  3. What order of translating, reflecting, and stretching do you think will be the easiest to use?

course folder If required, save a record of your discussion in your course folder.