Question

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.

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 given by $\frac{h(b)-h(a)}{b - a}$. Here, $a = 0$, $b = 3$.

Step2: Find $h(0)$ and $h(3)$ from the graph

From the graph, when $x = 0$, $h(0)=1$. When $x = 3$, $h(3)=8$.

Step3: Calculate the average rate of change

Substitute $h(0)=1$, $h(3)=8$, $a = 0$, and $b = 3$ into the formula: $\frac{h(3)-h(0)}{3 - 0}=\frac{8 - 1}{3}=\frac{7}{3}$.

Answer:

$\frac{7}{3}$