Question

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

Answer 1

`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...