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

( )f x x

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

2 3, 1( )

4, 0

x xf x

x x

Example 4 A Piecewise-Defined function

• Evaluate the function when x = -1, 0 and 1

2 1, 0( )

1, 0

x xf x

x x

• Sketch the Graph of

1, 4

( ) 25, 4

x xf x

x x

Sketch the Graph of

2

3 , 0

1, 0 1( )

, 1

x x

xf x

x x