Scenario: Taxi Fares - Explore function relationships through transportation costs!
A taxi charges $3 for the first mile and $1.50 for each additional mile. The total fare (y) depends on the number of miles traveled (x).
Function Rule: y = 1.5x + 3
| Miles (x) | Calculation | Fare (y) |
|---|---|---|
| 0 | 1.5(0) + 3 | $3.00 |
| 1 | 1.5(1) + 3 | $4.50 |
| 2 | 1.5(2) + 3 | $6.00 |
| 3 | 1.5(3) + 3 | $7.50 |
A function is a relationship where each input (x) has exactly one output (y). Think of it as a machine that takes a number and gives you back exactly one result.
Key Rule: For every x, there is exactly one y
Convert Celsius to Fahrenheit: F = 1.8C + 32
Function Table:
C = 0 → F = 32°F
C = 10 → F = 50°F
C = 20 → F = 68°F
C = 30 → F = 86°F
Area = side length squared: A = s²
Function Table:
s = 1 → A = 1 square unit
s = 2 → A = 4 square units
s = 3 → A = 9 square units
s = 4 → A = 16 square units
If the taxi fare is $12, how many miles did you travel?
Step 1: Set up the equation
12 = 1.5x + 3
Step 2: Solve for x
12 - 3 = 1.5x
9 = 1.5x
x = 6 miles
Answer: You traveled 6 miles.
A movie theater charges $8 for adults and $5 for children. Write a function rule for the total cost if a adults and c children attend.
Your function rule:
Using the taxi function y = 1.5x + 3, find the fare for 8 miles and determine how many miles you can travel with $15.
Your solution: