the graph of a function f is shown below. use the graph of the function to find its average rate of change…
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 = 3. simplify your answer as much as possible.
Answer
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, $a = 0$ and $b = 3$.
Step2: Find $f(0)$ and $f(3)$ from the graph
From the graph, when $x = 0$, $f(0)=2$; when $x = 3$, $f(3)=8$.
Step3: Calculate the average rate of change
Substitute $a = 0$, $b = 3$, $f(0)=2$, and $f(3)=8$ into the formula: $\frac{f(3)-f(0)}{3 - 0}=\frac{8 - 2}{3}=\frac{6}{3}=2$.
Answer:
2