this shows the graph of a function. what is the average rate of change of the function over the interval…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 3$.

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

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

Step3: Calculate the average rate of change

Substitute $a = 1$, $b = 3$, $f(1)=4$, $f(3)=2$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(3)-f(1)}{3 - 1}=\frac{2 - 4}{2}=\frac{-2}{2}=-1$.

Answer:

A. -1