Question

a rational function is given below.

$f(x)=\frac{4}{x - 2}$

what is the average rate of change of $f(x)$ over the interval $3\leq x\leq6$?

a. $-1$
b. $-3$
c. $1$
d. $3$

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here \(a = 3\), \(b=6\), and \(f(x)=\frac{4}{x - 2}\).

Step2: Calculate \(f(3)\) and \(f(6)\)

• For \(x = 3\): \(f(3)=\frac{4}{3-2}=4\)
• For \(x = 6\): \(f(6)=\frac{4}{6 - 2}=1\)

Step3: Substitute into the average - rate - of - change formula

\(\frac{f(6)-f(3)}{6 - 3}=\frac{1-4}{6 - 3}=\frac{-3}{3}=-1\)

Answer:

A. -1