4. find the average rate of change from x = 0 to x = 2.

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, $a = 0$, $b = 2$.

Step2: Determine $f(0)$ and $f(2)$ from the graph

From the graph, when $x = 0$, $y=f(0)=1$; when $x = 2$, $y=f(2)=4$.

Step3: Calculate the average rate of change

Substitute $a = 0$, $b = 2$, $f(0)=1$, and $f(2)=4$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(2)-f(0)}{2-0}=\frac{4 - 1}{2}=\frac{3}{2}$.

Answer:

$\frac{3}{2}$