Question

use the graph below to find the average rate of change of the function on the interval -3, 2.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-3\) and \(b = 2\).

Step2: Find \(f(-3)\) and \(f(2)\) from the graph

From the graph, when \(x=-3\), \(y = f(-3)=10\) (since the graph passes through the point \((-3,10)\)). When \(x = 2\), \(y=f(2)=10\) (since the graph passes through the point \((2,10)\)).

Step3: Substitute into the formula

Substitute \(f(-3)=10\), \(f(2)=10\), \(a=-3\), and \(b = 2\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{10-10}{2-(-3)}=\frac{0}{5}\).

Answer:

\(0\)