Lesson 4

1. Lesson 4

Mathematics 30-1 Module 1

Module 1: Function Transformations

Lesson 4: Combining Transformations

Focus

Some artwork is just one image manipulated over and over in slightly different ways. This graphic was made using stretches, reflections, and translations. Is it important in what order the transformations were applied? If you wanted to use a coordinate grid to help with these transformations, does it matter where you put the grid?

This picture shows two rows of identical heads facing each other. It appears that the rows go on forever into the distance. A large face looms over the rest of the heads.

In this lesson you will learn to use multiple transformations on a function. You will also learn to relate the graph of a transformed function to its equation.

Lesson Outcomes

At the end of this lesson you will be able to

sketch the graph of the function for given values of a, b, h, and k, given the graph of the function y = f(x)
write the equation of a function, given its graph, which is a translation and/or stretch of the graph of the function y = f(x)

Lesson Questions

You will investigate the following questions:

How can multiple transformations be applied to a function?
How can you write the equation of a transformed function given the original graph?

Assessment

Your assessment may be based on a combination of the following tasks:

completion of the Lesson 4 Assignment (Download the Lesson 4 Assignment and save it in your course folder now.)
course folder submissions from Try This and Share activities
additions to Formula Sheet

Materials and Equipment

graph paper