The function \( f(x) = -75x + 1,200 \) represents the value of your cell phone \( x \) months after you purchase it.
The initial value of the function occurs when \( x = 0 \), which corresponds to the time when you first purchase the cell phone. To find the initial value, we substitute \( x = 0 \) into the function:
\[ f(0) = -75(0) + 1,200 = 1,200 \]
The initial value of the function is \( 1,200 \).
Interpretation: This means that when you purchase the cell phone, its value is $1,200. This is the starting value of the cell phone before any depreciation (loss of value) begins to occur over time.