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, $a = 2$, $b = 5$.

Step2: Estimate function values from the graph

From the graph, when $x = 2$, $g(2)=- 4$. When $x = 5$, $g(5)=4$.

Step3: Calculate the average rate of change

Substitute $g(2)=-4$, $g(5)=4$, $a = 2$, and $b = 5$ into the formula: $\frac{g(5)-g(2)}{5 - 2}=\frac{4-(-4)}{3}=\frac{4 + 4}{3}=\frac{8}{3}$.

Answer:

$\frac{8}{3}$