The function is $\"\"$ .

To find the horizontal asymptote, evaluate the limit of the function as $\"\"$ and $\"\"$ .

$\"\"$

Now find the limit of the function as $\"\"$ .

$\"\"$

As $\"\"$ then $\"\"$ becomes $\"\"$ .

$\"\"$

Therefore the horizontal asymptotes are $\"\"$ and $\"\"$ .

Find the vertical asymptote.

Vertical asymptote appears when the function is not defined.

To find the vertical asymptote, equate denominator of the function to zero.

So $\"\"$ .

$\"\"$

It has no real roots.

Therefore there is no vertical asymptotes.

Verification :

Graph :

Graph the function $\"\"$ :

$\"\"$

Observe the graph.

There is no vertical asymptotes and horizontal asymptotes are $\"\"$ and $\"\"$ .

There is no vertical asymptotes.

The horizontal asymptotes are $\"\"$ and $\"\"$ .