Piecewise Functions
Objective:


Graph piecewise functions
Apply piecewise functions in a real world situational context
Warmup
With a partner, and having no prior guidance from me, try to graph the function below.
x 1
f ( x)   2
x
x0
y
x0
x
Summarize Below
What worked?
What did you do incorrectly that you want to avoid going forward?
Ex 1: Graph.
x  5

f ( x)  2 x  1
2 x  9

Key Points:
x  2
2  x  2
x2
y
x
Ex 2: Graph.
2 x  3

f ( x)  3
5

x0
x0
x0
y
x
Ex 3: Graph.
2 x  1

f ( x)  3
x  4

Now find:
f ( 4)
x0
0 x4
x4
f (1)
y
f (10)
x
Can you go backwards?
Write the equation for the piecewise defined functions shown below.
 _____
f ( x)  
 _____
_________
_________
Closure #1
A function and graph are shown below. Can you identify ALL the errors?
Applying Piecewise Functions
Example 1:
y
Cost of First Class Mail
Weight Not Over
1 ounce
2 ounces
3 ounces
4 ounces
5 ounces
Source: U.S. Postal Service
Cost
$0.45
0.65
0.85
1.05
1.25
x
y
Example 2:
Parking Garage Rates
$3 per half hour
$8 maximum for 12 hours
x
Example 3:
Wages - Write and graph a piecewise function that gives your weekly pay P in terms of the number of
hours, h, that you work.
y
You have a summer job that pays time
and a half for overtime. That is, if you
work more than 40 hours per week, your
hourly wage for the extra hours is 1.5
times your normal hourly wage of $8.
How much will you earn if you work
45 hours?
x