Question 115443
General Rule: 

To find the vertical asymptote:

Find the solutions for the denominator function. That solutions are the vertical asymptote. 

In our problem, denominator is x^2 + 2.

Consider the equation x^2 + 2 = 0

We get x^2 = -2

x = + or - sqrt{-2}

It has no real solution. ( since we cannot find a real number as the square root of -2)

So, the rational function does not have any vertical asymtote.

 
To find the horizontal asymtote: 

Find limit x tending to infinity f(x).

The limit value is the horizontal asymptote.

In our problem, Limit x tending to infinity f(x) = 0.

So, f(x) = y = 0 is the horizontal asymptote.


Finally, 

Horizontal: y = 0

Vertical : None.