Question

the graph of a function g is shown below. use the graph of the function to find its average rate of change from x = 0 to x = 2. simplify your answer as much as possible.

Explanation:

Step1: Recall 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, $a = 0$, $b = 2$.

Step2: Find $g(0)$ and $g(2)$ from the graph

From the graph, when $x = 0$, $g(0)=4$; when $x = 2$, $g(2)=16$.

Step3: Calculate the average rate of change

Substitute $g(0)=4$, $g(2)=16$, $a = 0$, and $b = 2$ into the formula: $\frac{g(2)-g(0)}{2 - 0}=\frac{16 - 4}{2}=\frac{12}{2}=6$.

Answer:

$6$