Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6 leq x leq -1$?

Explanation:

Step1: Recall the formula for average rate of change

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, \(a=-6\) and \(b = - 1\).

Step2: Find \(f(-6)\) and \(f(-1)\) from the graph

From the graph, when \(x=-6\), \(f(-6)=15\); when \(x = - 1\), \(f(-1)=0\).

Step3: Substitute values into the formula

Substitute \(a=-6\), \(b=-1\), \(f(a) = 15\), and \(f(b)=0\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{0 - 15}{-1-(-6)}=\frac{-15}{-1 + 6}=\frac{-15}{5}=-3\).

Answer:

\(-3\)