Module 1: Function Transformations

 

You have seen that multiple transformations can be applied to a function. By starting with the stretched and reflected equation y = af(bx), translations can be added by replacing y with y − k and x with x − h to give This is sometimes written as

 

You have also seen that switching the order of a translation and a stretch or a reflection affected the outcome of the transformation. To use an equation of the form apply the stretches and reflections before the translations.

 

This diagram shows y = f(x) with a right arrow leading to “stretch and reflect,” followed by a right arrow leading to “translate,” and, finally, followed by a right arrow leading to y – k = f(b(x – h)).

 

The next example shows how stretches and translations can be applied to the same function.


textbook

Read “Example 1” on pages 34 and 35 of the textbook.

 

 

 

Self-Check 1

 

Complete “Your Turn” from “Example 1” on page 35 of the textbook. Answer

Watch Graphing Transformations to see how a function of the form can be graphed from y = f(x).

 

 

This play button opens Graphing Transformations.



textbook

Read “Example 2” on page 36 of the textbook. Pay attention to how mapping notation is used to describe what happens to individual points.

 

Self-Check 2

  1. Complete “Your Turn” from “Example 2” on page 37 of the textbook. Answer
  2. Complete “Check Your Understanding” questions 2, 3, 6.a., 6.b., and 7 on pages 38 to 40 of the textbook. Answer