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

Answer:

$\frac{3}{2}$

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

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

From the graph, when $x=-3$, $f(-3)=- 4$; when $x = 1$, $f(1)=2$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(1)-f(-3)}{1-(-3)}=\frac{2-(-4)}{1 + 3}=\frac{2 + 4}{4}=\frac{6}{4}=\frac{3}{2}$.