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 ≤ 5?
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 $\frac{f(b)-f(a)}{b - a}$, where $a = 2$ and $b = 5$.
Step2: Read function values from the graph
From the graph, when $x = 2$, $f(2)=4$; when $x = 5$, $f(5)= - 8$.
Step3: Calculate the average rate of change
Substitute $a = 2$, $b = 5$, $f(2)=4$, and $f(5)=-8$ into the formula: $\frac{f(5)-f(2)}{5 - 2}=\frac{-8 - 4}{3}=\frac{-12}{3}=-4$.
Answer:
$-4$