Lesson 2: Analyzing Rational Functions

Focus

When preparing goods for transport, the cost of packaging is one factor to consider. Typically, packaging in bulk is cheaper. Can you think of some reasons for this?

One measure of efficiency of packaging is the volume-to-surface-area ratio of the container. This ratio increases as the size of the container increases. This means that if you double the volume, you will require less than double the amount of packaging if the package shape remains the same. This is one reason packaging in bulk is cheaper. While modelling the volume-to-surface-area ratio, you will see that more than one type of “break” is possible in the graph of a function.

In this lesson you will explore how some rational functions can have discontinuities that are not asymptotes.

Lesson Outcomes

At the end of this lesson you will be able to

• describe what a discontinuity is
• explain the difference between an asymptote and a point of discontinuity and determine when each will occur

Lesson Question

You will investigate the following question:

• How can you determine when a discontinuity will occur in a function and what kind of discontinuity it will be?

Assessment

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

• completion of the Lesson 2 Assignment (Download the Lesson 2 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms