Hector would like to join a gym that has a one-time membership fee plus a monthly fee. He can use the function f(x)=35x+50

Question

Hector would like to join a gym that has a one-time membership fee plus a monthly fee. He can use the function  f(x)=35x+50
  to model the cost of gym membership after  x
  months. Identify and interpret the initial value of the function.(1 point)
Responses

The initial value of 50 represents the monthly fee.
The initial value of 50 represents the monthly fee.

The initial value of 35 represents the monthly fee.
The initial value of 35 represents the monthly fee.

The initial value of 35 represents the one-time membership fee.
The initial value of 35 represents the one-time membership fee.

The initial value of 50 represents the one-time membership fee.
The initial value of 50 represents the one-time membership fee.

GPT-4o mini · Answer

The correct interpretation of the initial value in the function $ f(x) = 35x + 50 $ is:

The initial value of 50 represents the one-time membership fee.

In this function, $ x $ represents the number of months, $35 is the monthly fee, and $50 is the one-time membership fee. Therefore, when $ x = 0 $ (indicating the beginning, or at the time of joining), the cost $ f(0) = 35(0) + 50 = 50 $, which is the one-time fee Hector pays to join the gym.