Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-8leq xleq -6$?

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, \(a=-8\) and \(b = -6\).

Step2: Find \(f(-8)\) and \(f(-6)\) from the graph

From the graph, when \(x=-8\), \(y=-12\) (so \(f(-8)=-12\)), and when \(x = -6\), \(y = 4\) (so \(f(-6)=4\)).

Step3: Substitute into the formula

Substitute \(a=-8\), \(b=-6\), \(f(a)=-12\), and \(f(b) = 4\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{4-(-12)}{-6-(-8)}=\frac{4 + 12}{-6 + 8}=\frac{16}{2}\).

Answer:

\(8\)