1.6 Step and Piecewise Functions. Objective To identify and graph step and piecewise- defined functions.

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Presentation transcript:

1.6 Step and Piecewise Functions

Objective To identify and graph step and piecewise- defined functions.

Step Functions Functions whose graphs resemble set of stairsteps are known as step functions.

The most famous of the step functions is the greatest integer function. This function is denoted by

Definition The greatest integer function equals the greatest integer less than or equal to x.

Example A parking lot in downtown Houston charges $2.00 for the first hour and $1.00 for each additional hour. Graph the charges as a function of time. How much does it cost to park for 8 hours and 35 minutes.

A function defined by two or more equations over a specified domain is called a piecewise function.

Example 4 A Piecewise-Defined function Graph the function

Example 4 A Piecewise-Defined function Evaluate the function when x = -1, 0 and 1

Sketch the Graph of