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 \(x=-6\), \(y=-10\) (so \(f(-6)=-10\)), and when \(x = - 1\), \(y=-10\) (so \(f(-1)=-10\)).

Step3: Substitute into the formula

Substitute \(a=-6\), \(b=-1\), \(f(a)=-10\), and \(f(b)=-10\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-10-(-10)}{-1-(-6)}=\frac{-10 + 10}{-1 + 6}\).

Step4: Simplify the expression

\(\frac{-10 + 10}{-1 + 6}=\frac{0}{5}=0\).

Answer:

\(0\)