Question

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
f
(
x
)
=
35
x
+
50
to model the cost of gym membership after x
x
months. Identify and interpret the initial value of the function.(1 point)
Responses

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

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 one-time membership fee.

Answer 1

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

- \( 35x \) accounts for the monthly fee of $35 for each month.
- The constant term \( 50 \) represents the one-time membership fee.

Thus, the initial value of the function, which occurs when \( x = 0 \) (the starting point before any months have passed), is \( f(0) = 35(0) + 50 = 50 \).

Therefore, the correct interpretation is:

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