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, $a=-1$ and $b = 3$.

Step2: Find $f(-1)$ and $f(3)$ from the graph

From the graph, when $x=-1$, $f(-1)=0$; when $x = 3$, $f(3)=4$.

Step3: Calculate the average rate of change

Substitute $a=-1$, $b = 3$, $f(-1)=0$, and $f(3)=4$ into the formula: $\frac{f(3)-f(-1)}{3-(-1)}=\frac{4 - 0}{3+1}=\frac{4}{4}=1$.

Answer:

$1$