the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 1$.

Step2: Find $f(-1)$ and $f(1)$ from the graph

From the graph, when $x=-1$, $f(-1)= - 8$; when $x = 1$, $f(1)=-8$.

Step3: Calculate the average rate of change

Substitute $a=-1$, $b = 1$, $f(-1)=-8$ and $f(1)=-8$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(1)-f(-1)}{1-(-1)}=\frac{-8-(-8)}{1 + 1}=\frac{-8 + 8}{2}=0$.

Answer:

$0$