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Function Value Interpretation

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Function Value Interpretation

Read each function rule carefully. Explain what the input and output mean in the situation. For the select-all question, choose every correct statement.

Real-World Function Interpretation

1.A bike rental costs R(h) = 7h + 5 dollars for h hours. What does R(4) = 33 mean?

Renting a bike for 4 hours costs $33.
Renting a bike for 33 hours costs $4.
The bike travels 33 miles in 4 hours.
The rental costs $4 each hour.

2.A classroom printer has printed N(m) = 40m pages after m minutes. What does N(9) = 360 tell you?

The printer takes 360 minutes to print 9 pages.
After 9 minutes, the printer has printed 360 pages.
The printer prints 9 pages every 360 minutes.
The printer began with 360 pages already printed.

3.A garden center's earnings are E(p) = 12p + 30 dollars after selling p plant pots. Select all statements that correctly interpret E(5) = 90.

Selling 5 pots brings in $90 in earnings.
The garden center earns $90 for each pot sold.
E(5) gives the earnings when the number of pots sold is 5.
The garden center sold 90 pots to earn $5.

4.A distance function is D(t) = 48t, where t is the number of hours a train travels and D is distance in miles. State what the input and output represent.

Interpreting Function Values

5.A streaming service charges S(w) = 3w + 8 dollars for w weeks of access. Explain the meaning of S(6) = 26.

6.A reservoir's water volume is W(t) = 9t + 120 gallons, where t is the number of minutes water has been added. Interpret W(8) = 192 and explain what the value at t = 0 represents.

7.A workshop tracks the number of wooden toys made, A(h), after h hours. Explain what A(0) = 35 means, then describe how production changes in the data.

Hours, h

Toys made, A(h)

105

175

245

8.A greenhouse model is G(d) = 3d + 64°F, where d is the number of days since tracking began. Write an interpretation of G(10) = 94.

Apply Your Understanding

9.Invent a real-world situation in which f(8) = 60 makes sense. Name what the function measures, what 8 represents, and what 60 represents.

10.A small business models its daily profit with P(x) = 18x - 240 dollars, where x is the number of items sold. If P(20) = 120, interpret this value and explain how it compares with the break-even point.