Question

the graph of a function $f$ 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 $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b=2$.

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

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

Step3: Calculate the average rate of change

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

Answer:

6