Scenario: Transportation Costs - Learn the basics of functions through taxi fare calculations!
A taxi charges $3.50 as a base fare plus $2.25 per mile. Create a function to calculate the total cost for any number of miles.
Function: f(x) = 3.50 + 2.25x
Where x = number of miles traveled
Function Definition: A function is a relationship where each input (x) has exactly one output (f(x)).
Key Rule: For every x, there is exactly one y
Let's calculate the taxi fare for different distances using f(x) = 3.50 + 2.25x
| Miles (x) | Calculation | Total Cost f(x) |
|---|---|---|
| 0 | 3.50 + 2.25(0) | $3.50 |
| 1 | 3.50 + 2.25(1) | $5.75 |
| 2 | 3.50 + 2.25(2) | $8.00 |
| 3 | 3.50 + 2.25(3) | $10.25 |
| 5 | 3.50 + 2.25(5) | $14.75 |
How much does a 4-mile taxi ride cost?
f(4) = 3.50 + 2.25(4)
f(4) = 3.50 + 9.00 = $12.50
If the fare is $20, how far did you travel?
20 = 3.50 + 2.25x
16.50 = 2.25x
x = 7.33 miles
Function Notation: f(x) = 3.50 + 2.25x
Using f(x) = 3.50 + 2.25x, find f(6)
Your solution:
A parking garage charges $2.00 base fee plus $1.50 per hour. Create a function and table for 0, 1, 2, 3, and 4 hours.
Your function and table: