12 given the graph, find the average rate of change from x = 1 and x = 3. the average rate of change is

Explanation:

Step1: Recall the average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x=a$ to $x = b$ is given by $\frac{g(b)-g(a)}{b - a}$. Here, $a = 1$, $b = 3$.

Step2: Find the function values from the graph

From the graph, when $x = 1$, $g(1)=0$; when $x = 3$, $g(3)=4$.

Step3: Calculate the average rate of change

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

Answer:

2