Function Value Interpretation

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📊 Part 1: Reading Function Values in Context

Scenario: A taxi company charges based on distance traveled. The function f(x) represents the total cost in dollars, where x is the distance in miles.

1. If f(3) = 12, what does this mean in the context of the taxi ride?

The taxi travels 12 miles in 3 minutes

A 3-mile ride costs $12

The taxi costs $3 per 12 miles

The ride takes 12 hours for 3 miles

2. For a manufacturing company, g(x) represents the total cost in hundreds of dollars to produce x units. If g(5) = 8, this means:

It costs $8 to produce 5 units

It costs $800 to produce 5 units

It takes 8 hours to produce 5 units

5 workers can produce 8 units

3. A temperature function h(t) gives the temperature in °F after t hours. If h(6) = 78, what does the 78 represent?

4. For a distance function d(t) where t is time in hours, if d(2) = 120, write a complete sentence explaining what this means.

📈 Part 2: Interpreting Function Tables

Scenario: The table below shows the cost of renting a car for different numbers of days.

5. Based on the pattern, what does f(4) = 180 tell us about car rental?

6. If this rental company's function is f(x) = 45x, explain what the number 45 represents in this real-world context.

7. A student says "f(0) = 0 means you get the car for free on day zero." Is this interpretation correct? Explain your reasoning.

🔍 Part 3: Real-World Function Analysis

Scenario: A water tank is being filled. The function w(t) = 50 + 8t represents the amount of water (in gallons) after t minutes.

8. Calculate w(10) and explain what this value means in the context of filling the water tank.

Interpretation: ________________________________________________

9. What does the 50 in the function equation represent in this real-world situation?

10. If w(15) = 170, write a complete sentence explaining what happened after 15 minutes.

11. A friend says "The function value tells us the rate of change." Do you agree or disagree? Explain your thinking.

Function Value Interpretation

Function Value Interpretation

📊 Part 1: Reading Function Values in Context

📈 Part 2: Interpreting Function Tables

🔍 Part 3: Real-World Function Analysis

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