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 = 1 to x = 4. simplify your answer as much as possible.

the graph of a function h is shown below. use the graph of the function to find its average rate of change from x = 1 to x = 4. simplify your answer as much as possible.

Answer

Explanation:

Step1: Recall 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, $a = 1$, $b = 4$.

Step2: Determine function values from graph

From the graph, when $x = 1$, $h(1)=4$; when $x = 4$, $h(4)=16$.

Step3: Calculate rate of change

Substitute into the formula: $\frac{h(4)-h(1)}{4 - 1}=\frac{16 - 4}{3}$.

Step4: Simplify the result

$\frac{16 - 4}{3}=\frac{12}{3}=4$.

Answer:

4