Function Value Interpretation

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📊 Part 1: Real-World Function Interpretation

1. A taxi company charges according to the function C(d) = 2.50d + 3.00, where d is distance in miles and C is cost in dollars. What does C(8) = 23 mean in this situation?

The taxi travels 23 miles in 8 minutes

It costs $23 to travel 8 miles

The taxi costs $8 for 23 miles

The taxi travels 8 miles per hour

2. The temperature function T(h) = 65 + 15h represents temperature in °F after h hours of heating. If T(3) = 110, what does this tell us?

After 3 hours, the temperature is 110°F

It takes 110 hours to reach 3°F

The temperature increases by 110°F every 3 hours

The starting temperature is 110°F

3. A factory's production function is P(t) = 50t + 200, where t is time in hours and P is total items produced. Which statements about P(6) = 500 are correct?

After 6 hours, 500 items have been produced

The factory produces 500 items per hour

In the first 6 hours of operation, total production is 500 items

The factory started with 500 items already made

4. For the distance function D(t) = 60t representing miles traveled after t hours at constant speed, what does the input represent and what does the output represent?

Input represents: _________________ Output represents: _________________

✏️ Part 2: Function Value Analysis

5. The cost function for a phone plan is C(m) = 0.15m + 25, where m is minutes used and C is total cost in dollars. Interpret the meaning of C(200) = 55 in complete sentences.

6. A water tank is being filled according to V(t) = 12t + 80, where V is volume in gallons and t is time in minutes. If V(15) = 260, explain what this means and what it tells us about the tank.

7. Look at this manufacturing data: M(h) represents items produced after h hours.
M(0) = 50, M(2) = 150, M(4) = 250, M(6) = 350
Explain what M(0) = 50 means and describe the pattern you observe.

8. The temperature in a greenhouse follows T(d) = 2d + 68, where d is days since monitoring began and T is temperature in °F. If today is day 12 and T(12) = 92, write a real-world interpretation of this function value.

🧠 Part 3: Critical Thinking

9. Create your own real-world scenario where f(10) = 75 makes sense. Describe what the function represents, what the input and output mean, and explain the significance of this function value.

10. A company's profit function is P(x) = 15x - 200, where x is number of items sold. If P(20) = 100, explain why this function value is significant for the business and what it tells us about their break-even point.