Question

A video game club charges a fixed annual membership fee of $20 and $2 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $15 the next year?
f(n) = 2n + 35
f(n) = 20n + 2
f(n) = 10n + 35
f(n) = 2n + 10

Answer 1

The total cost for video rental, f(n), is the sum of the membership fee and the cost of renting video game. The latter is the product of cost per video game times n video games. The correct equation used to represent the total cost is,
                          f(n) = 20 + 2n
Since the membership is increased by 15, the new equation is,
                          f(n) = 35 + 2n

Answer 2

Since f(n) is a function of both the annual membership fee and the rental fee, then the total annual cost f(n) is the sum of both fees. Where n is the number of video games rented, "2n" represents the rental fee, and "35" represents the membership fee. Therefore:

f(n) = 2n + 35