a rational function is given below.\n\n$f(x)=\\frac{4}{x - 2}$\n\nwhat is the average rate of change of…

a rational function is given below.\n\n$f(x)=\\frac{4}{x - 2}$\n\nwhat is the average rate of change of $f(x)$ over the interval $3\\leq x\\leq6$?\n\na. $-1$\nb. $-3$\nc. $1$\nd. $3$

a rational function is given below.\n\n$f(x)=\\frac{4}{x - 2}$\n\nwhat is the average rate of change of $f(x)$ over the interval $3\\leq x\\leq6$?\n\na. $-1$\nb. $-3$\nc. $1$\nd. $3$

Answer

Answer:

A. -1

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)