The document discusses piecewise functions and provides examples of how to write piecewise functions to model real-world scenarios involving non-continuous functions. It includes 5 word problems that require writing piecewise functions to represent situations involving pay rates, cell phone plans, candy prices, car rentals, and internet service plans. The problems cover domains, ranges, and calculating costs based on the piecewise functions.

1. Piecewise Functions
Use the piecewise function below to answer each question.


h( x ) = 


Step 1
Step 2
Step 3
What is the range for step 1?
What is the range for step 2?
What is the range for step 3?
What is the domain for the entire function?
What is h(
)?
What is h(
What is h(
)?
)?
What is h(
What is h(
)?
)?
MSL Sample (Guide 2013)

2. Piecewise Functions
The function below determines the amount of yearly tax a person must pay,
which is based on the amount of money they earn each year.
0.10 x

T ( x ) = 0.07( x − 12,750 ) + 765
0.0775( x − 60,000 ) + 4,072.50

$ 0 ≤ x < 12,750
12,750 ≤ x < 60,000
x ≥ $ 60,000
a. Describe the domain and range of the tax function in context.
b. Identify the domain and range of t(x).
c. Based on the function provided, explain how the amount of tax owed
changes if your earnings increase from $10,000 to $50,000.
MSL Sample

3. Piecewise Functions
1. Write and graph a piecewise function for the parking charges shown on the sign.
2. What are the domain and range of the function?
WEEKEND RATES
$3 per half hour
$8 MAX for 12 hours
Word Problem Creation

4. Piecewise Functions
Piecewise Word Problems
1.You have a summer job that pays time and a half for overtime. (If you work over 40 hours)
After that it is 1.5 times your hourly rate of $7.00/hr.
a. Write a piecewise function to represent this problem.
b. How much money do you make if you work 45 hours.
Word Problem Creation

5. Piecewise Functions
2. Your cell phone plan costs $75/month and gives you unlimited talk, and 500 text messages
per month, and no data plan. After 500 text messages, it costs $.10 per text you send.
a. Write a piecewise function to represent this situation.
b. How much will it cost if you send 750 text messages.
Word Problem Creation

6. Piecewise Functions
3. You go to Ingles to buy some candy. You decide to buy snickers because they have them on
special. A bag of snickers costs $3.45, but if you buy 4 or more bags, they only cost $3.00 per
bag. Write a piecewise function to represent this situation
Word Problem Creation

7. Piecewise Functions
4. A car rental company charges a flat fee of $45 to rent a car. In addition to that you must pay
a fee per day you rent it. If you keep the car for 3 days or less, it costs $7 per day. If you keep
the car longer than 3 days it only costs $5 per day.
a. Write a piecewise function to represent this situation
b. How much does it cost to rent for 3 days? 4 days? What is weird about this?
Word Problem Creation

8. Piecewise Functions
5. One ISP (Internet Service Provider) has the following rate schedule for high speed internet
service.
Monthly Service Charge - $18.00
First 50 Hours of Usage - Free
Next 50 hours of Usage - $0.25/hour
Over 100 hours of Usage - $1.00/hour
a. Write a piecewise function to represent this situation. Be Careful. Remember if you use 51
hours, you will only be charged for one hour because the first 50 are free. Check your work
b. How much would you be charged
Word Problem Creation

9. Piecewise Functions
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10. Piecewise Functions
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