Question

A student borrowed $480 from a friend. He agreed to make monthly payments of $96 with no interest until the loan balance was paid off. The function shown models this situation, where f(x) represents the remaining loan balance in dollars after the student has made x monthly payments. f(x) = 480 − 96x Which statements are true about the domain and range of the function for this situation?

Answer 1

The domain and function in this situation is

The domain is [0, 5]

The range is [0, 480]

How to find the domain and range

The domain of a function is the set of all possible input values. In this case, x represents the number of monthly payments.

The range of a function is the set of all possible output values. Here, the function represents the remaining loan balance after x monthly payments.

The possible x values for y = 0 (when the loan is fully paid)

0 = 480 − 96x

96x = 480

x = 480 / 96

x = 5

Since the student can make any non negative integer number of monthly payments, the domain is [0, 5]

The range starts from 480 to 0