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Function Notation in Context

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Function Notation in Context

Read each function rule carefully. Use the input value shown to find the output, and explain what the result means in the situation.

Reading Function Notation

1.A bowling alley charges $9 per game, plus a one-time $4 shoe-rental fee. The total cost is modeled by C(g) = 9g + 4, where g is the number of games. What does C(3) represent?

The cost of three bowling alleys
The total cost of bowling three games, including shoe rental
The number of games that cost $3
The cost of renting shoes for three people

2.A greenhouse's temperature is modeled by T(h) = 72 + 2h, where T is the temperature in degrees Fahrenheit and h is the number of hours after the heater is switched on. What does T(5) = 82 mean?

3.A bike rental costs R(m) = 7 + 5m dollars for m hours. Find R(4), and state what your answer represents.

4.In a function that gives the total pay for a shift, which could reasonably be an input? Select all that apply.

Number of hours worked
Hourly pay rate
Total pay in dollars
Employee's shoe size

Connecting Rules to Situations

5.Create a real-world situation modeled by f(x) = 6x. State what x and f(x) represent.

6.Using your situation for f(x) = 6x, find f(7) and explain what the result means in that situation.

7.A delivery van travels at a constant rate, modeled by D(t) = 48t, where t is time in hours and D(t) is distance in miles. Complete: D(2) = .

8.For the delivery van modeled by D(t) = 48t, complete: After 2 hours, the van has traveled miles.

9.For the delivery van modeled by D(t) = 48t, complete: If D(t) = 192, then t = .

10.For the delivery van modeled by D(t) = 48t, complete: The van takes hours to travel 192 miles.

Function Notation Challenge

11.A fundraiser's net earnings are modeled by E(n) = 14n − 120, where n is the number of gift baskets sold and E(n) is the earnings in dollars after expenses. Explain what −120 represents, calculate E(15), explain what E(15) means, and state what it means when E(n) = 0.

12.Write a real-world function using function notation. Identify the input and output, then show one calculation using an input of your choice.