How to find the asymptotes of #f(x) = (x^2+1)/(x^2-1)# ?

1 Answer
Apr 11, 2016

Answer:

#x=+-1 and y=1#.

Explanation:

#y = f(x) = 1 +2/(x^2-1)#, by actual division

As # xto+-1, ytooo#.
As #yto1, xto+-oo#.
So, the lines #x = +-1 and y = 1# are asymptotic to the graph of y = f(x)

The graph is symmetrical about the y-axis.

It cuts y-axis at #(0, -1)#.

For #y > 1, x < -1#, for one branch, and #x > 1#, for another..

In brief, there are three branches. Two above y=1 are asymptotic to all the three asymptotes. The third through# (0, -1)i# is asymptotic to y = 1 only...