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, $a = 7$, $b = 8$.

Step2: Read function values from the graph

From the graph, when $x = 7$, $g(7)=0$; when $x = 8$, $g(8)= - 4$.

Step3: Calculate the average rate of change

Substitute $g(7)=0$, $g(8)= - 4$, $a = 7$, and $b = 8$ into the formula: $\frac{g(8)-g(7)}{8 - 7}=\frac{-4-0}{1}=-4$.

Answer:

$-4$