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 0 ≤ 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, $a = 0$ and $b = 4$.
Step2: Find $f(0)$ and $f(4)$ from the graph
From the graph, when $x = 0$, $y=f(0)=12$; when $x = 4$, $y = f(4)=2$.
Step3: Calculate the average rate of change
Substitute $a = 0$, $b = 4$, $f(0)=12$ and $f(4)=2$ into the formula: $\frac{f(4)-f(0)}{4 - 0}=\frac{2 - 12}{4}=\frac{-10}{4}=-\frac{5}{2}$.
Answer:
$-\frac{5}{2}$