The function f(x)=−75x+1,200

Question

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.(1 point)
Responses

The initial value of 1,200 represents the value of your cell phone at the time you purchase it.
The initial value of 1,200 represents the value of your cell phone at the time you purchase it.

The initial value of 1,200 represents the monthly cost of your phone.
The initial value of 1,200 represents the monthly cost of your phone.

The initial value of 75 represents the monthly cost of your phone.
The initial value of 75 represents the monthly cost of your phone.

The initial value of 75 represents the value of your cell phone at the time you purchase it.

GPT-4o mini · Answer

The correct interpretation of the initial value of the function $ f(x) = -75x + 1,200 $ is:

The initial value of 1,200 represents the value of your cell phone at the time you purchase it.

This is because the initial value corresponds to the value of the function when $ x = 0 $, which would reflect the value of the cell phone at the moment of purchase. In this case, when $ x = 0 $:

\[ f(0) = -75(0) + 1,200 = 1,200 \]

Thus, the initial value of 1,200 indicates that the cell phone is worth $1,200 right at the time it is purchased.