Introduction

Have you ever seen a graph like this one?

Probably not. All of the functions you have worked with up to this point have been continuous. Continuous graphs are those that do not have a break or gap. This graph is called a piecewise function because it is made up of several different pieces.

Piecewise functions are used for several applications in the real-world, such as pricing different options of rental vehicles, prices of stamps or shipping, and selling merchandise that have different sizes.

In this lesson, you will learn about linear functions and piecewise functions that have two or three pieces, such as the one above.

 

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Create equations in one variable and use them to solve problems.
  • Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • Graph piece-wise defined functions.

Enduring Understandings

  • Operations create relationships between numbers.
  • The language of mathematics is communicated through specialized vocabulary and symbols used to represent and describe mathematical ideas, generalizations, and relationships.
  • By describing patterns using mathematics, we can make predictions and generalizations, analyze situations in everyday life, and sort and classify things.

The above objectives correspond with the Alabama Course of Study Algebra II and Algebra II with Trig standards: 20 and 21

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