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 ≤ x ≤ -3?

Explanation:

Step1: Recall average - rate - of - change formula

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 $b = - 3$.

Step2: Find $f(-6)$ and $f(-3)$ from the graph

From the graph, when $x=-6$, $y = f(-6)=0$. When $x=-3$, $y = f(-3)= - 10$.

Step3: Calculate the average rate of change

Substitute $f(-6)=0$, $f(-3)=-10$, $a=-6$, and $b=-3$ into the formula: $\frac{f(-3)-f(-6)}{-3-(-6)}=\frac{-10 - 0}{-3 + 6}=\frac{-10}{3}=-\frac{10}{3}$.

Answer:

$-\frac{10}{3}$