Date post: | 01-Jan-2016 |
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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