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 = - 1 to x = 5.
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, \(a=-1\) and \(b = 5\).

Step2: Find \(h(-1)\) and \(h(5)\) from the graph

From the graph, when \(x=-1\), \(h(-1)=8\); when \(x = 5\), \(h(5)=8\).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 5\), \(h(-1)=8\), and \(h(5)=8\) into \(\frac{h(b)-h(a)}{b - a}\). We get \(\frac{8 - 8}{5-(-1)}=\frac{0}{6}\).

Answer:

\(0\)