Question

A-Plus Rentals, a truck rental company, charges a rental fee of $25 plus $0.30 per mile for driving between 0 and 500 miles for

the standard-sized truck. For the same truck, the company charges $100 plus $0.15 per mile for driving more than 500 miles, but
less than 1000 miles.
Write a step function that represents the situation.

Answer 1

y = .3x + 25 {x l if 0 < x < 500}

y = .15x + 100 {x l if 500 < x < 1000}

Explanation:

The only thing that I am not sure about is the 500 miles. For the first part we are told if the miles are between 0 and 500. 500 is not between, so it is not included in the first equation, but it 500 does not appear to be included in the second equation either. It pertains to miles more than 500. 500 is not more than 500. So, it looks like 500 miles is not covered in either equation.

Answer 2

Explanation:

Let's define the step function f(x) that represents the situation:

For 0 ≤ x ≤ 500:

f(x) = 0.30x + 25

For 500 < x < 1000:

f(x) = 0.15x + 100

In this step function, x represents the number of miles driven, and f(x) represents the total cost of renting the truck for that distance. The function has two separate cases based on the mileage range:

- For distances between 0 and 500 miles, the rental fee is $25 plus $0.30 per mile driven. Hence, the equation is f(x) = 0.30x + 25.

- For distances greater than 500 miles but less than 1000 miles, the rental fee is $100 plus $0.15 per mile driven. The equation becomes f(x) = 0.15x + 100.

By using this step function, you can calculate the rental cost for different mileage ranges.