How do you find the Vertical, Horizontal, and Oblique Asymptote given #y = (x + 1)/(x - 1)#?

1 Answer
Feb 7, 2017

Answer:

The vertical asymptote is #x=1#
The horizontal asymptote is #y=1#
No oblique asymptote

Explanation:

As you cannot divide by #0#, #x!=1#

The vertical asymptote is #x=1#

As the degree of the numerator #=# the degree of the denominator, there is no oblique asymptote

#lim_(x->+oo)y=lim_(x->+oo)x/x=1#

The horizontal asymptote is #y=1#

graph{(y-(x+1)/(x-1))(y-1)(y-100x+100)=0 [-8.1, 9.674, -4.8, 4.085]}