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 2 ≤ x ≤ 4?
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, $a = 2$ and $b = 4$.
Step2: Find $f(2)$ and $f(4)$ from the graph
From the graph, when $x = 2$, $f(2)=4$; when $x = 4$, $f(4)=0$.
Step3: Calculate the average rate of change
Substitute $a = 2$, $b = 4$, $f(2)=4$, and $f(4)=0$ into the formula: $\frac{f(4)-f(2)}{4 - 2}=\frac{0 - 4}{2}=\frac{-4}{2}=-2$.
Answer:
$-2$