In the function \( f(x) = 35 \), where \( f(x) \) represents the cost of gym membership after \( x \) months, the function indicates a fixed monthly fee of $35.
To identify the initial value of the function, we need to evaluate \( f(0) \), which represents the cost of the gym membership at the start, or after 0 months:
\[ f(0) = 35 \]
Interpretation: The initial value of the function, \( f(0) = 35 \), means that Hector would incur a cost of $35 at the beginning of his gym membership. Since the function only represents the monthly fee and does not account for a one-time membership fee, it implies that Hector would need to pay $35 immediately when he joins the gym for the first month. If there is an additional one-time membership fee, that would need to be specified separately.