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 -8 ≤ x ≤ -6?
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, $a=-8$ and $b = - 6$.
Step2: Find $f(-8)$ and $f(-6)$ from the graph
From the graph, when $x=-8$, $f(-8)=-8$; when $x = - 6$, $f(-6)=4$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(-6)-f(-8)}{-6-(-8)}=\frac{4 - (-8)}{-6 + 8}=\frac{4 + 8}{2}=\frac{12}{2}=6$.
Answer:
6