This module is for Algebra 1, Grades 7-12 Welcome

Mathematics is the study of patterns and deviations from those patterns. Graphs, equations and tables are representations we can use to study patterns, and to better understand data from real-life situations.

For example, the graph shown represents the income earned by Melanie as she completes her shift at Burger Works. After she works 40 hours, Melanie receives a bonus and begins to earn overtime pay.

This graph can be used to answer such questions as: How much money does Melanie make per hour? Once Melanie reaches 40 hours, how much does she make per hour in overtime? How much is the bonus she receives? How much money will Melanie make if she works 75 hours?

The graph to the right is a piecewise function. Notice how the graph of the situation is literally in two pieces. In this module, you will learn how to graph piecewise functions and use the graphs to solve real-world problems.

Module Objective

By the end of this module, you will be able to:

  • Graph a variety of piecewise functions.
  • Use the graphs of different types of piecewise functions to model and solve real-world problems.
waitress serving a burger and fries A coordinate grid, with x axis labeled Hours and extending from 0 to 80 in increments of 10, and with y axis labeled income in dollars extending from 0 to 800 in increments of 50. The graph is titled Melanie’s Income. A line extends from the origin to the solid dot at (40, 300). A second line begins at the open dot at (40, 400) and extends up with a slope of 10.


  • Recognize the function families contained within a piecewise function.
  • Identify the domain and range over which a given piecewise function is defined.
  • Model a piecewise function algebraically, graphically, numerically and verbally.