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 $-8leq xleq -3$?
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 $b = - 3$.
Step2: Find $f(-8)$ and $f(-3)$ from the graph
From the graph, when $x=-8$, $f(-8)=0$; when $x = - 3$, $f(-3)=20$.
Step3: Calculate the average rate of change
Substitute $a=-8$, $b=-3$, $f(-8)=0$, and $f(-3)=20$ into the formula: $\frac{f(-3)-f(-8)}{-3-(-8)}=\frac{20 - 0}{-3 + 8}=\frac{20}{5}=4$.
Answer:
$4$