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 4 ≤ x ≤ 6?
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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b = 6$.
Step2: Read function values from the graph
From the graph, when $x = 4$, $f(4)=8$; when $x = 6$, $f(6)=0$.
Step3: Calculate the average rate of change
Substitute $f(4)=8$, $f(6)=0$, $a = 4$, and $b = 6$ into the formula: $\frac{f(6)-f(4)}{6 - 4}=\frac{0 - 8}{2}=\frac{-8}{2}=-4$.
Answer:
$-4$