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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-6$ and $b = - 3$.

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

From the graph, when $x=-6$, $f(-6)=-30$. When $x = - 3$, $f(-3)=-20$.

Step3: Calculate the average rate of change

Substitute $a=-6$, $b=-3$, $f(-6)=-30$ and $f(-3)=-20$ into the formula: $\frac{f(-3)-f(-6)}{-3-(-6)}=\frac{-20 - (-30)}{-3 + 6}=\frac{-20 + 30}{3}=\frac{10}{3}$.

Answer:

$\frac{10}{3}$