Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 2 ≤ x ≤ 8?

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b = 8$.

Step2: Find $f(2)$ and $f(8)$ from the graph

From the graph, when $x = 2$, $y=f(2)=0$; when $x = 8$, $y = f(8)=25$.

Step3: Calculate the average rate of change

Substitute $a = 2$, $b = 8$, $f(2)=0$, and $f(8)=25$ into the formula: $\frac{f(8)-f(2)}{8 - 2}=\frac{25-0}{6}=\frac{25}{6}$.

Answer:

$\frac{25}{6}$