Question

You buy x bottles of soda for $1.50 using a gift card that you got as a reward for getting good grades

on your last report card. Your gift card's original balance was $15. The function f(x) = $15-$1.50
represents the amount of money you have left on the card after your purchase. What is the domain of
the function? Explain your reasoning.

Answer 1

`0\leq x \leq 10`

Explanation:

The function is
`f(x)=15-1.50x` where x is the number of bottles of soda.

The domain means the set of "allowed" x values.

Also, f(x) means the amount of money left, which cannot be less than 0. So we put 0 into f(x) and solve for x:

`f(x)=15-1.5x\\0=15-1.5x\\1.5x=15\\x=(15)/(1.50)\\x=10`

This means the highest number of bottles you can buy is 10. So the domain is anything from 0 to 10. You can buy 0 until highest 10 bottles. Hence the domain is

`0\leq x \leq 10`