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 the formula for average rate of change

The formula for 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 \(x = 0\), \(h(0)=3\); when \(x = 3\), \(h(3)=10\).

Step3: Substitute values into the formula

Substitute \(a = 0\), \(b = 3\), \(h(0)=3\), and \(h(3)=10\) into \(\frac{h(b)-h(a)}{b - a}\). We get \(\frac{h(3)-h(0)}{3-0}=\frac{10 - 3}{3}\).

Step4: Simplify the expression

\(\frac{10 - 3}{3}=\frac{7}{3}\).

Answer:

\(\frac{7}{3}\)