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 $-8leq xleq -7$?
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 $b = - 7$.
Step2: Find $f(-8)$ and $f(-7)$ from the graph
From the graph, when $x=-8$, $f(-8)=-8$; when $x = - 7$, $f(-7)=0$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(-7)-f(-8)}{-7-(-8)}=\frac{0 - (-8)}{-7 + 8}=\frac{8}{1}=8$.
Answer:
8