2-2: Piecewise Functions2-2: Piecewise Functions2-2: Piecewise Functions2-2: Piecewise Functions

Unit 2: Linear FunctionsUnit 2: Linear FunctionsEnglish CasbarroEnglish Casbarro

Piecewise Functions Piecewise functions have different

range values depending on the domain values that are used.

For instance, a movie theater could charge $5.00 for all children 12 and under, $9.00 for everyone between 13 and 55, and give a senior citizen discount price of $6.50 to everyone 55 and over.

The graph of such a function would look like this:

The table of values would look like this:

So, depending on your age, thePrice of your ticket would vary.

This is the equation for the example you just saw. This is a step function, since the range is all constant values.

Create a table of values and a verbal description of the following graph.

A step function has a constant value for each member of the domain. Not all piecewise functions are constants, but there is one that you should know. The greatest integerfunction is denoted by [x] and is graphed as the greatest integer not greater than the number shown.

A truck driver earns $21.00 per hour for the first 40 hours of work per week. The driver earns time-and-a-half, or $31.50 for each hour of overtime. The pay that the driver will earn can be shown by the function below.

Example 3

There are 2 different equations that you would graph, depending on the domain values used.

Graph each of the following functions.