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 $-3leq xleq7$?
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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$ and $b = 7$.
Step2: Find $f(-3)$ and $f(7)$ from the graph
From the graph, when $x=-3$, $f(-3)=0$. When $x = 7$, $f(7)=-40$.
Step3: Calculate the average rate of change
Substitute $a=-3$, $b = 7$, $f(-3)=0$, and $f(7)=-40$ into the formula: $\frac{f(7)-f(-3)}{7-(-3)}=\frac{-40 - 0}{7 + 3}=\frac{-40}{10}=-4$.
Answer:
$-4$