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, $a=-2$ and $b = 4$.

Step2: Estimate function values from the graph

From the graph, when $x=-2$, assume $g(-2)=0$ (by looking at the $y$ - value of the graph at $x=-2$). When $x = 4$, assume $g(4)=0$ (by looking at the $y$ - value of the graph at $x = 4$).

Step3: Calculate the average rate of change

Substitute $a=-2$, $b = 4$, $g(-2)=0$, and $g(4)=0$ into the formula $\frac{g(b)-g(a)}{b - a}$. We get $\frac{g(4)-g(-2)}{4-(-2)}=\frac{0 - 0}{4 + 2}=\frac{0}{6}=0$.

Answer:

$0$