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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 1$.

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

From the graph, when $x=-1$, $f(-1)= - 10$; when $x = 1$, $f(1)=10$.

Step3: Calculate the average rate of change

Substitute $a=-1$, $b = 1$, $f(-1)=-10$ and $f(1)=10$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(1)-f(-1)}{1-(-1)}=\frac{10-(-10)}{1 + 1}=\frac{10 + 10}{2}=\frac{20}{2}=10$.

Answer:

$10$