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Function Value Interpretation

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Function Value Interpretation

Read each function rule or table carefully. Explain what the input and output mean in the situation.

Interpreting Function Values

For the questions in this section, inputs and outputs represent quantities in different situations, such as rental time and cost, time and temperature, or time and distance.

1.If r(4) = 28, which statement correctly explains the function value?

A 4-hour bicycle rental costs $28.
A bicycle is rented for $4 over 28 hours.
The bicycle travels 28 miles in 4 hours.
The rental costs $4 for each of 28 bicycles.

2.A print shop's function p(x) gives the cost in dollars to print x posters. If p(6) = 15, what does 15 represent?

The shop prints 15 posters for $6.
Printing 6 posters costs $15.
It takes 15 hours to print 6 posters.
Each poster costs $6.

3.A function T(m) gives the temperature, in degrees Fahrenheit, m minutes after an oven is turned on. If T(12) = 250, what does 250 describe?

4.A hiking app uses d(t) for the distance, in miles, walked after t hours. Write a sentence explaining d(3) = 7.5.

Reading a Function Table

The table shows the total price of renting a kayak. The input is rental time in hours; the output is the price in dollars.

Rental time, h

Total price, $

5.Using the kayak rental table, explain what f(5) = 90 means.

6.The kayak rental price is modeled by f(x) = 18x, where x is the number of rental hours. What does 18 mean in this situation?

7.A renter says, “f(0) = 0 means I can use a kayak for free.” Is that a reasonable conclusion from the rule f(x) = 18x? Explain what f(0) actually tells you and what it does not tell you.

Function Rules in Context

A rain barrel contains 24 gallons of water to start. Water flows into it at 6 gallons per minute. The rule V(t) = 24 + 6t gives the amount of water V, in gallons, after t minutes.

8.Use V(t) = 24 + 6t to find V(8). Then explain what your answer means for the rain barrel.

9.In the rule V(t) = 24 + 6t, what does the number 24 represent?

10.The rule gives V(11) = 90. Write a sentence interpreting this function value in the rain-barrel situation.

11.A classmate says, “A function value always tells you the rate of change.” Do you agree? Use V(t) = 24 + 6t to distinguish the function value V(5) from the rate of change.