Find where the expression is undefined.

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

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 horizontal asymptote is the line where and .

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.

No Vertical Asymptotes

Horizontal Asymptotes:

No Oblique Asymptotes

Find the Asymptotes y=(4x^2)/(2x^2+1)