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 ≤ 4?

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 $b = 4$.

Step2: Find $f(-6)$ and $f(4)$ from the graph

From the graph, when $x=-6$, $f(-6)=8$. When $x = 4$, $f(4)=-8$.

Step3: Calculate the average rate of change

Substitute $a=-6$, $b = 4$, $f(-6)=8$ and $f(4)=-8$ into the formula: $\frac{f(4)-f(-6)}{4-(-6)}=\frac{-8 - 8}{4 + 6}=\frac{-16}{10}=-\frac{8}{5}$.

Answer:

$-\frac{8}{5}$