Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -2 leq x leq 3 )?

Explanation:

Step1: Find the values of \(f(-2)\) and \(f(3)\)

From the graph, when \(x = - 2\), \(f(-2)=-40\); when \(x = 3\), \(f(3)=40\).

Step2: Use the average - rate - of - change formula

The formula for the average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-2\), \(b = 3\), \(f(a)=f(-2)\) and \(f(b)=f(3)\).
Substitute the values into the formula: \(\frac{f(3)-f(-2)}{3-(-2)}=\frac{40-(-40)}{3 + 2}\)

$$=\frac{40 + 40}{5}=\frac{80}{5}$$

Answer:

\(16\)