Question

he function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-8\leq x\leq -7$?

Explanation:

Step1: Find the values of \(f(-8)\) and \(f(-7)\)

From the graph, when \(x = - 8\), \(y=f(-8)=0\); when \(x=-7\), \(y = f(-7)=2\).

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, \(a=-8\), \(b = - 7\), \(f(a)=f(-8)=0\), \(f(b)=f(-7)=2\).
Substitute into the formula: \(\frac{f(-7)-f(-8)}{-7-(-8)}=\frac{2 - 0}{-7 + 8}\).

Answer:

\(2\)