question the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on…
question the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -3 ≤ x ≤ 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, $a=-3$ and $b = 3$.
Step2: Find $f(-3)$ and $f(3)$ from the graph
From the graph, when $x=-3$, $f(-3)=0$. When $x = 3$, $f(3)=50$.
Step3: Calculate the average rate of change
Substitute $a=-3$, $b = 3$, $f(-3)=0$ and $f(3)=50$ into the formula: $\frac{f(3)-f(-3)}{3-(-3)}=\frac{50 - 0}{3+3}=\frac{50}{6}=\frac{25}{3}$.
Answer:
$\frac{25}{3}$