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 given by $\frac{g(b)-g(a)}{b - a}$. Here, $a=-7$ and $b = 1$.

Step2: Determine $g(-7)$ and $g(1)$ from the graph

From the graph, when $x=-7$, $g(-7)=7$; when $x = 1$, $g(1)=1$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{g(1)-g(-7)}{1-(-7)}=\frac{1 - 7}{1+7}=\frac{-6}{8}=-\frac{3}{4}$.

Answer:

$-\frac{3}{4}$