the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…
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?
Answer
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 $b = 4$.
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 into the formula: $\frac{f(4)-f(-6)}{4-(-6)}=\frac{-8-(-8)}{4 + 6}=\frac{-8 + 8}{10}=0$.
Answer:
$0$