the graph of a function f 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 $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b = 5$.

Step2: Read function values from the graph

From the graph, when $x = 2$, $f(2)=- 2$; when $x = 5$, $f(5)=6$.

Step3: Calculate the average rate of change

Substitute $a = 2$, $b = 5$, $f(2)=-2$, and $f(5)=6$ into the formula: $\frac{f(5)-f(2)}{5 - 2}=\frac{6-(-2)}{3}=\frac{6 + 2}{3}=\frac{8}{3}$.

Answer:

$\frac{8}{3}$