The function f(x)=−75x+1,200 represents the value of your cell phone x months after you purchase it. Identify and interpret the initial value of the function.
The initial value of the function, as represented by the equation f(x) = -75x + 1,200, is 1,200. The initial value of the function refers to the starting value or the value when x is equal to 0.
Interpreting this, it means that immediately after purchasing your cell phone (when x is 0 months), the value of the cell phone is $1,200.
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To identify the initial value of the function, you need to find the y-intercept of the function f(x). The y-intercept is the value of f(x) when x is zero.
In this case, the function is f(x) = -75x + 1200. So, to find the initial value, substitute x = 0 into the function:
f(0) = -75(0) + 1200
= 0 + 1200
= 1200
Therefore, the initial value of the function is 1200.
Interpreting the initial value in the context of the problem, it means that when you purchase your cell phone (at x = 0 months), its value is $1200.