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 ≤ -2?

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 $b = - 2$.

Step2: Find $f(-6)$ and $f(-2)$ from the graph

From the graph, when $x=-6$, $y = f(-6)=-30$. When $x=-2$, $y = f(-2)=20$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(-2)-f(-6)}{-2-(-6)}=\frac{20 - (-30)}{-2 + 6}=\frac{20 + 30}{4}=\frac{50}{4}=12.5$.

Answer:

$12.5$