How do you find vertical, horizontal and oblique asymptotes for #(X^2)/( X-1)#?

1 Answer
Apr 16, 2016

Answer:

Vertical asymptote of #(X^2)/(X-1)# is given by #x-1=0#.
and oblique asymptote is #y=x#

Explanation:

The vertical asymptotes of #(X^2)/(X-1)# are given by zeros of denominator i.e. #x-1=0#.

As the degree of numerator is just one higher than that of denominator, there is no horizontal asymptote, but we do have a slant asymptote given by #y=(X^2)/X=X#.

The slant asymptote is given by #y=x#

graph{(x^2)/(x-1) [-15, 15, -15, 15]}