1. Lesson 6

Mathematics 30-1 Module 7

Module 7: Rational Functions and Function Operations

 

Lesson 6: Composition of Functions

 
Focus

 

In this photo a delivery truck is part of the busy traffic on a freeway.

iStockphoto/Thinkstock

 This diagram shows that time of day and amount of traffic are related and that amount of traffic and driving time are related, and asks if time of day and driving time are related.

 

In a large city, suppose that a delivery truck regularly drives between a furniture store and a warehouse. The length of time required to make the trip depends on the amount of traffic on the streets. The amount of traffic depends on the time of day.

 

Clearly, there is a relationship between the length of driving time and the time of day. How can the relationship between driving time and amount of traffic and the relationship between amount of traffic and time of day be used to describe the relationship between driving time and time of day?

 

In this lesson you will explore how one function can be used as the input for another function. This process is called a composition of functions.

 

Lesson Outcomes

 

At the end of this lesson you will be able to

  • determine the composition of two functions
  • determine the equation of a composite function
  • sketch the graph of a composite function
Lesson Question

 

You will investigate the following question:

  • How can the composition of functions be used to simplify problems?
Assessment

 

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

  • completion of the Lesson 6 Assignment (Download the Lesson 6 Assignment and save it in your course folder now.)
  • course folder submissions from Try This and Share activities
  • additions to Glossary Terms and Formula Sheet
  • work under Project Connection