Question

If f(x)=(4x-6)/x , what is the average rate of change of f(x) over the interval [-3, 6]?А.1/3В.1/9 C. -1/3D. -3

Answer 1

C. -1/3

Step-by-step explanation:

Given the function:

`f(x)=(4x-6)/(x)`

To determine the average rate of change of f(x) over the interval [-3, 6]:

First, we evaluate f(-3) and f(6):

`\begin{gathered} f(-3)=(4(-3)-6)/(-3)=(-12-6)/(-3)=(-18)/(-3)=6 \\ f(6)=(4(6)-6)/(6)=(24-6)/(6)=(18)/(6)=3 \end{gathered}`

The average rate of change over [-3,6] is:

`\begin{gathered} \text{Rate}=(f(-3)-f(6))/(-3-6) \\ =(6-3)/(-3-6) \\ =(3)/(-9) \\ =-(1)/(3) \end{gathered}`

The correct choice is C.