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 ≤ 3?

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 $b = 3$.

Step2: Find $f(2)$ and $f(3)$ from the graph

From the graph, when $x = 2$, $y=f(2)=20$; when $x = 3$, $y = f(3)=80$.

Step3: Calculate the average rate of change

Substitute $f(2)=20$, $f(3)=80$, $a = 2$, and $b = 3$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(3)-f(2)}{3 - 2}=\frac{80 - 20}{1}=60$.

Answer:

60