Question

find the average rate of change over the given interval. 2. 0<x<3

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 3$.

Step2: Estimate function values from the graph

From the graph, when $x = 0$, $y=f(0)=0$; when $x = 3$, $y=f(3)=7$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(3)-f(0)}{3 - 0}=\frac{7 - 0}{3}=\frac{7}{3}$.

Answer:

A. $\frac{7}{3}$