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 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.

1 answer

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.