the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b = 5$.

Step2: Find $f(2)$ and $f(5)$ from the graph

From the graph, when $x = 2$, $y=f(2)= - 10$. When $x = 5$, $y=f(5)=5$.

Step3: Calculate the average rate of change

Substitute $f(2)=-10$, $f(5) = 5$, $a = 2$, and $b = 5$ into the formula: $\frac{f(5)-f(2)}{5 - 2}=\frac{5-(-10)}{3}=\frac{5 + 10}{3}=\frac{15}{3}=5$.

Answer:

$5$