SOLUTION: how to solve the x- and y- and asymptotes of these rational functions? {{{y=(x^2+1)/(x-3)}}} {{{y=(1/6)(x-1)^3(x+2)^2(6-x)}}} {{{y=(2x+1)/(5-3x)}}} please explain, Th

Algebra ->  Functions -> SOLUTION: how to solve the x- and y- and asymptotes of these rational functions? {{{y=(x^2+1)/(x-3)}}} {{{y=(1/6)(x-1)^3(x+2)^2(6-x)}}} {{{y=(2x+1)/(5-3x)}}} please explain, Th      Log On


   

Question 912127: how to solve the x- and y- and asymptotes of these rational functions?
y=%28x%5E2%2B1%29%2F%28x-3%29
y=%281%2F6%29%28x-1%29%5E3%28x%2B2%29%5E2%286-x%29
y=%282x%2B1%29%2F%285-3x%29
please explain,
Thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your second equation with the 1%2F6 factor is a polynomial and has no asymptotes.

Your third equation has horizontal asymptote of -2%2F3 toward the left and -2%2F3 toward the right; which you can tell by seeing degree of numerator and denominator are the same and examining each extreme case. A vertical asymptote is for 5-3x=0 meaning x=5%2F3 is the vertical asymptote.

First equation is undefined for x=3 so this is the vertical asymptote. Degree of numerator is one more than degree of denominator, so ... you can find the slant asymptote; perform the division and consider what happens to the remainder for x extreme in either direction. The quotient tells you the slant asymptote.