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

Answer:

C. -1/3

Explanation:

Given the function:

$f(x)=\frac{4x-6}{x}$

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

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

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

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

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

The correct choice is C.