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, $a=-4$ and $b=-1$.

Step2: Estimate function values from graph

From the graph, when $x=-4$, $f(-4)=-4$ and when $x = - 1$, $f(-1)=4$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(-1)-f(-4)}{-1-(-4)}=\frac{4-(-4)}{-1 + 4}=\frac{4 + 4}{3}=\frac{8}{3}$.

Answer:

$\frac{8}{3}$