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

Question 912127: how to solve the x- and y- and asymptotes of these rational functions?

please explain,
Thank you
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Your second equation with the factor is a polynomial and has no asymptotes.

Your third equation has horizontal asymptote of toward the left and 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 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.
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