3. what is the average rate of change of f(x) from x = 1 to x = 3? m -6 r 3 p -2 s 6

Explanation:

Step1: Recall the 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, $a = 1$, $b = 3$.

Step2: Estimate $f(1)$ and $f(3)$ from the graph

From the graph, when $x = 1$, $f(1)=0$; when $x = 3$, $f(3)=6$.

Step3: Calculate the average rate of change

Substitute $a = 1$, $b = 3$, $f(1)=0$, and $f(3)=6$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(3)-f(1)}{3 - 1}=\frac{6 - 0}{2}=\frac{6}{2}=3$.

Answer:

R. 3