A food order at a restaurant is paid for with a $10 bill. What function represents the difference between the cost of the food and the change returned? Assume that this difference is nonnegative.

A: f(x) = |2x -10|

Huh

f(x) = 10 - x

How did you end up with that answer?

I misread it

cost = 10 - change
cost - change = 10 - 2 change

How would I graph this?

just put in a bunch of cost values from 0 to 10

if the cost were $2
change = 8
cost - change = 2 - 8 = -6
and
10 - 2(8) = -6

It is only non-negative if the cost is between 5 and 10

To determine the function that represents the difference between the cost of the food and the change returned, we need to break down the problem.

Let's assume that the cost of the food is represented by the variable "x."

The change returned would be equal to the amount paid (represented by the $10 bill) minus the cost of the food (x). This can be written as 10 - x.

However, we need to ensure that the difference is nonnegative, meaning that if the cost of the food is higher than the amount paid, we consider that there is no change and the difference would be zero.

To express this in mathematical terms, we can use the absolute value function to ensure that the value is nonnegative. So, the function that represents the difference between the cost of the food and the change returned can be written as:

f(x) = |10 - x|