x2 64 11 Let fx x211x18 a Find the horizontal asymptotes of

x2- 64 11. Let fx)- x2-11x+18 a. Find the horizontal asymptotes of fx). b. Find the vertical asymptotes of f(x). c. Find the slant asymptotes of f(x). d. Find the holes in the graph of f(x). e. Find linnx), f. Find lim f(x). -- x2

Solution

11. f(x) = (x²-64)/(x²-11x +18)=(x+8)(x-8)/(x-8)(x-3)= (x+8)/(x-3)

Horizontal asymptote

Here degree of numerator = degree of denoinator

Therefore, HA, y= numerator\'s leading coefficient/ denominator\'s leading coefficient

         y=1/1=1

b. x-3=0

x=3

c. THere is no slant asymptote since degree of numerator and denominator are same .

d. hole is at x-8=0

x=8