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

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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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