Question

find the average rate of change of ( g(x) ) below on the interval ( -3,3 ). average rate of change =

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = g(x)\) on the interval \([a,b]\) is \(\frac{g(b)-g(a)}{b - a}\). Here, \(a=-3\) and \(b = 3\).

Step2: Find \(g(-3)\) and \(g(3)\) from the graph

From the graph, when \(x=-3\), \(g(-3)=0\); when \(x = 3\), \(g(3)=0\).

Step3: Substitute into the formula

Substitute \(a=-3\), \(b = 3\), \(g(-3)=0\), and \(g(3)=0\) into \(\frac{g(b)-g(a)}{b - a}\). We get \(\frac{0-0}{3-(-3)}=\frac{0}{6}\).

Answer:

\(0\)