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 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: Read function values from graph
From the graph, when $x = 2$, assume $f(2)=2$ (by looking at the $y$ - value of the graph at $x = 2$). When $x = 4$, assume $f(4)=14$ (by looking at the $y$ - value of the graph at $x = 4$).
Step3: Calculate average rate of change
Substitute $a = 2$, $b = 4$, $f(2)=2$ and $f(4)=14$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(4)-f(2)}{4 - 2}=\frac{14 - 2}{2}=\frac{12}{2}=6$.
Answer:
6