AFDA – Unit 3: Absolute Value and Piecewise Functions Name: _________________
Day 7 Notes: Three Piecewise and Word Problems
Block: _____ Date:_______
Today…
 You will learn how to graph piecewise functions that have three pieces
 You will learn how to write piecewise functions from a word problem
Let’s review what we did last class:
x  2
f ( x)  
3x  3
3,
 1
1.) f ( x)   x  1,
 2
4 x  4,
 x  4,

2.) f ( x)  1,
 x  2,

x  3
x  3
x  2
2  x  0
x0
x 1
1  x  1
x  1

3 x  3,

3.) f ( x)  2,
 1
 x  1,
 2
1,
2,
4.) f ( x)  
3,
4,
x0
0 x2
x2
2  x  0
0 x2
2 x4
4 x6
5.) You have a summer job that pays “time and a half” for overtime (if you work more
than 40 hours). You make $7.00/hour.
a.) Write a piecewise function that gives your weekly pay, P, in terms of the
number of hours you work, h.
b.) How much will you make if you work 45 hours?
6.) The amount of Social Security tax you pay, depends on your annual income. In
2015, you pay 6.2% of your income if it is less than $118,500. If your income is at
least 118,500, you pay a fixed amount of $7,347.
a.) Write a piecewise function that gives the Social Security tax.
b.) The median household income in Loudoun County is $116,848. How much
would a family that makes the median income pay in Social Security tax? Round
to the nearest cent.
7.) You decide to design and order PFHS shirts for the homecoming game this year.
The t-shirt printing shop charges an initial charge of $20 to create the silk screen, then
$17.00 per shirt for orders of 50 or fewer shirts and $15.80 per shirt for orders of more
than 50 shirts.
a.) Write a piecewise function that gives the cost, C, for an order of x amount of
shirts.
b.) If 80 people wanted to buy the shirt, how much would it cost?
c.) BONUS: How much would you need to charge for each shirt to break even?