the graph of a function g 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 $y = g(x)$ from $x=a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-1$ and $b = 2$.

Step2: Read function values from the graph

From the graph, when $x=-1$, $g(-1)=8$; when $x = 2$, $g(2)=5$.

Step3: Calculate the average rate of change

Substitute $g(-1)=8$, $g(2)=5$, $a=-1$, and $b = 2$ into the formula: $\frac{g(2)-g(-1)}{2-(-1)}=\frac{5 - 8}{2+1}=\frac{-3}{3}=-1$.

Answer:

$-1$