the graph of a function $f$ is shown below. use the graph of the function to find its average rate of change…

the graph of a function $f$ is shown below. use the graph of the function to find its average rate of change from $x = - 4$ to $x = 2$. simplify your answer as much as possible.

the graph of a function $f$ is shown below. use the graph of the function to find its average rate of change from $x = - 4$ to $x = 2$. simplify your answer as much as possible.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-4$ and $b = 2$.

Step2: Determine $f(-4)$ and $f(2)$ from the graph

From the graph, when $x=-4$, $f(-4)=8$; when $x = 2$, $f(2)=-4$.

Step3: Calculate the average rate of change

Substitute $f(-4)=8$, $f(2)=-4$, $a=-4$, and $b = 2$ into the formula: $\frac{f(2)-f(-4)}{2-(-4)}=\frac{-4 - 8}{2+4}$.

Step4: Simplify the expression

$\frac{-4 - 8}{2+4}=\frac{-12}{6}=-2$.

Answer:

$-2$