Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Find where the expression is undefined.

Consider the rational function where is the degree of the numerator and is the degree of the denominator.

1. If , then the x-axis, , is the horizontal asymptote.

2. If , then the horizontal asymptote is the line .

3. If , then there is no horizontal asymptote (there is an oblique asymptote).

Find and .

Since , the x-axis, , is the horizontal asymptote.

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

Horizontal Asymptotes:

No Oblique Asymptotes

Vertical Asymptotes:

Horizontal Asymptotes:

No Oblique Asymptotes

Graph xy=4