the graph of a function (h) is shown below. use the graph of the function to find its average rate of change…
the graph of a function (h) 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 $y = h(x)$ from $x=a$ to $x = b$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 0$ and $b=3$.
Step2: Find $h(0)$ and $h(3)$ from the graph
From the graph, when $x = 0$, $h(0)=4$; when $x = 3$, $h(3)=10$.
Step3: Calculate the average rate of change
Substitute $h(0)=4$, $h(3)=10$, $a = 0$, and $b = 3$ into the formula: $\frac{h(3)-h(0)}{3 - 0}=\frac{10 - 4}{3}=\frac{6}{3}=2$.
Answer:
2