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 1 ≤ 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, $a = 1$, $b = 3$.
Step2: Find $f(1)$ and $f(3)$ from the graph
From the graph, when $x = 1$, $f(1)=4$; when $x = 3$, $f(3)= - 4$.
Step3: Calculate the average rate of change
Substitute $a = 1$, $b = 3$, $f(1)=4$, and $f(3)=-4$ into the formula: $\frac{f(3)-f(1)}{3 - 1}=\frac{-4 - 4}{2}=\frac{-8}{2}=-4$.
Answer:
$-4$