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

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

Answer 1

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

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

In this function, the term \( 50 \) is the constant, which indicates the cost incurred at \( x = 0 \) (i.e., before any months of membership have passed). The term \( 35x \) represents the monthly fee \( (35) \) multiplied by the number of months \( (x) \). Since there are no months yet, the cost at \( x = 0 \) is solely the one-time membership fee of \( 50 \).