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 ≤ 5?

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 $b = 5$.

Step2: Find $f(-6)$ and $f(5)$ from the graph

From the graph, when $x=-6$, $y = f(-6)=0$. When $x = 5$, $y=f(5)=-20$.

Step3: Calculate the average rate of change

Substitute $f(-6)=0$, $f(5)=-20$, $a=-6$ and $b = 5$ into the formula: $\frac{f(5)-f(-6)}{5-(-6)}=\frac{-20 - 0}{5 + 6}=\frac{-20}{11}$.

Answer:

$-\frac{20}{11}$