Learning Resources

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Outcomes

In this lesson you will learn

• to construct and analyze the graphs of piecewise functions

Students will be expected to:

• explore and describe the connections between continuity, limits, and functions
• demonstrate an intuitive understanding of the concept of limit
• demonstrate an understanding for the conceptual foundations of limit, the area under a curve, the rate of change, and the slope of the tangent line, and their applications
• model problem situations with combinations and compositions of functions
• use tables and graphs as tools to interpret expressions
• evaluate and apply limits

Introduction

Your work with the absolute-value function in the previous section enabled you to see it as piecewise. This section is designed to illustrate the fact that piecewise functions can comprise various types over different parts of the domain, and not just linear functions.

This is a relatively short section requiring about an hour for completion.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• right and left hand limits
• interval notation
• how to determine if a function is continuous
• points of discontinuity