Function Notation in Context

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📚 Part 1: Interpreting Function Notation

1. A movie theater charges $12 per ticket plus a $3 convenience fee per order. The function C(t) = 12t + 3 represents the total cost in dollars for t tickets. What does C(5) represent?

The cost of 5 movie theaters

The total cost for 5 tickets

The number of tickets that cost $5

The cost per ticket when buying 5

2. The function T(h) = 68 - 3h gives the temperature in °F at h hours after midnight. What does T(8) = 44 mean in this context?

3. A car rental company charges using the function P(m) = 25 + 0.15m, where P is the total cost in dollars and m is miles driven. Calculate P(200) and explain what it means.

4. Which of the following could represent the input (x-value) in a real-world function? Check all that apply:

Number of hours worked

Temperature in degrees

Total cost in dollars

Distance traveled in miles

✏️ Part 2: Creating Context

5. The function f(x) = 8x represents a relationship in a real-world situation. Create a context (story) where this function makes sense. What do x and f(x) represent?

My context: ________________________________________________

x represents: _______________________________________________

f(x) represents: ___________________________________________

6. For your context in question 5, what would f(6) equal and what does it mean?

f(6) = ______

This means: ________________________________________________

7. A function is written as D(t) = 55t, where D represents distance in miles and t represents time in hours. Fill in the blanks:

D(3) = _____ means that after _____ hours, the distance traveled is _____ miles.

If D(t) = 220, then t = _____, which means it takes _____ hours to travel _____ miles.

🎯 Part 3: Function Notation Challenge

8. A bakery's profit function is P(c) = 15c - 200, where c is the number of cakes sold and P is profit in dollars.

a) What does the -200 represent in this context? _________________________

b) Calculate P(20): ____________

c) Explain what P(20) means: ____________________________________

d) What does it mean if P(c) = 0? ___________________________________

9. Write your own real-world function using proper function notation. Include what the input and output represent, then give an example calculation.

Function Notation in Context

Function Notation in Context

📚 Part 1: Interpreting Function Notation

✏️ Part 2: Creating Context

🎯 Part 3: Function Notation Challenge

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