Question

Problem 2 Score: /25 Identify all asymptotes for the following functions. Even if a function possesses no asymptotes of a certain type, please state so explicitly (e.g, if f(x) for instance has no vertical asymptotes, please state this in your final answer). a (12 points): f(1) = (2-1)(3+3)

Answer 1

Given function is fix= x244x+3 = (x+3)(x) = 2 real (x2-1)(x+3) (x2-1)(ers) The line Vertical asymptotes on of function fre), the limit x=L is a xatical anymphotes the function (one sided, at स no this point is enfmite. in other words, it mean that possible panty point there the denominator equals o does not exist. So fried the find denominator equals o and check them 25-3 =-1 limit is frete xs-3+ x-1 4 check another limit lis 22+4x+3 182-1)(x+3) X-3 = dulte Since limit is finite, then x=-3 is not a valical lim £ & lim onymphale. x2+4x+3 x = -1 ta = -Y x-lt x-2 x9-17 (22+3)(x+1) Since limit is finite, then x=-1 is not a vatical anymptole. line a x 17 x- Since limit is unfinite, then azt is vertical asymptle

Line Horizontal Anympholes ; ģ=4 horizontal anymptote- of function y = frie) lim f(x)=L or lim frx)=L and Lis frite. is a ce either X1 Xt-co len (22+ = o 20 & Calculate the limit 22+4* +3 lim (-) (x+3)(x2-1) lim a 2+4x+3 lim (-1) = 0 x+3)(x2-1) Thus, the horizontal anymptote es y =o. xt-co Slant Anymptots Since the degue of the newerater one degene greater than the denominator, slant anympholes. then es not there is ho Annulee Vatical anymptoles Horizontal Anymptolen :y=0 i2=1 No Slant Asymptole.