This graph shows Andre biking to his friend’s house, where he hangs out for a while. Then they bike together to the store to buy some groceries before racing back to Andre’s house for a movie night. Each line segment in the graph represents a different part of Andre’s travels.

Graph composed of 5 linear sections. Horizontal axis, time, vertical axis, distance from home. Beginning at the origin, first segment slopes up as it moves right. Second segment horizontal, third segment slopes up and right, more steeply than the first segment. Fourth segment horizontal, fifth segment slopes down and right back to the horizontal axis.

This is an example of a piecewise linear function, which is a function whose graph is pieced together out of line segments. It can be used to model situations in which a quantity changes at a constant rate for a while, then switches to a different constant rate.

We can use piecewise functions to represent stories, or we can use them to model actual data. In the second example, temperatures recorded at different times throughout a day are modeled with a piecewise function made up of two line segments. Which line segment do you think does the best job of modeling the data?

Scatterplot, horizontal, time in hours after midnight, 0 to 12 by ones, vertical, temperature in degrees Fahrenheit. Fifty points approximate a straight line from point 2 5 comma 50 increasing to 5 point 75 comma 59 and then decreasing from there to 12 comma 52 point 5.