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

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$ and $b = 4$.

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

From the graph, when $x=-2$, $f(-2)=3$. When $x = 4$, $f(4)=3$.

Step3: Calculate the average rate of change

Substitute $f(-2)=3$, $f(4)=3$, $a=-2$, and $b = 4$ into the formula: $\frac{f(4)-f(-2)}{4-(-2)}=\frac{3 - 3}{4 + 2}=\frac{0}{6}=0$.

Answer:

$0$