Introduction to Functions
Name: Date: Period:
1. An electrician works at a job site at a rate of $40 per hour or any portion of an hour. In other words, he will charge you $40 as soon as he comes up to the first hour, and then $40 for the second hour, etcetera.
a) Graph the amount the electrician charges, c, in dollars
as a function of the number of hours he works.
b) How much does he charge for working 3.5 hours?
Circle the point on the graph the shows this answer.
2. A step function is defined using the piecewise formula[pic].
(a) Evaluate the following:
[pic] [pic]
[pic] [pic]
(b) Graph f(x) on the grid to the right.
(c) State the domain and range of this function.
Domain: Range:
3. The step function g(x) is shown on the grid to below. Answer the following questions.
(a) Evaluate each of the following:
[pic] [pic]
[pic] [pic]
b) Ji Hwan states that the range of this function is [pic].
Is he correct? Why or why not.
c) Write an equation for this step function.
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Step and Piecewise Review
4. Stewart International Airport in Newburgh, New York charges for parking the way many airports do, by the partial hour. Their short-term parking rates are shown below.
a) What would the function look like. Explain why the
total amount you will pay for parking at Stewart is a
step function based onthe number of hours you’ve
parked?
b) How much would you have to pay if you parked for
5 hours and 22 minutes? Show how you determined
your answer.
c) After how many hours of parking will you hit the maximum charge of $30? Explain your reasoning.
5. Graph the function defined by:
[pic]
(b) State the range of the function f(x).
6. Southeast Electric charges $0.09 per kilowatt-hour for the first 200 kWh. The company charges $0.11 per kilowatt-hour for all electrical usage in excess of 200 kWh.
a) Write a piecewise function.
b) How many kilowatt-hours were used if a monthly electric bill was $57.05?
7. A construction worker earned $17 per hour for the first 40 hours of work and $25.50 per hour for work in excess of 40 hours.
a) Write a piecewise function.
b) One week he earned $896.75. How much overtime did he work?
Step and Piecewise Review
-----------------------
Charge, c, $
Hours worked
1
5
4
3
2
100
200
y
x
y
x
Stewart International Airport Rates & Information
Parking Lots and Rates at SWF Airport (including tax)
Stewart On-Airport Short-Term Lot
1 hr or part thereof $3
Each additional hour or part thereafter* $3
24-hr maximum $30
*charges are incurred in hour increments before reaching the daily maximum
y
x
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