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 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.

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.

Answer 1

The function \( f(x) = 35x + 50 \) represents the cost of gym membership after \( x \) months, where:

• \( 35x \) is the variable cost depending on the number of months (with \( 35 \) being the monthly fee),
• \( 50 \) is the fixed cost or one-time membership fee.

The initial value of the function, which occurs when \( x = 0 \), is \( f(0) = 35(0) + 50 = 50 \).

Thus, the correct interpretation is:

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