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 $x=-6$, $f(-6)= - 80$ and when $x = 4$, $f(4)=60$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(4)-f(-6)}{4-(-6)}=\frac{60-(-80)}{4 + 6}=\frac{60 + 80}{10}=\frac{140}{10}=14$.

Answer:

14