# Precalculus Examples

Step 1

Find where the expression is undefined.

Step 2

Since as from the left and as from the right, then is a vertical asymptote.

Step 3

Since as from the left and as from the right, then is a vertical asymptote.

Step 4

List all of the vertical asymptotes:

Step 5

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).

Step 6

Find and .

Step 7

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

Step 8

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

Step 9

This is the set of all asymptotes.

Vertical Asymptotes:

Horizontal Asymptotes:

No Oblique Asymptotes

Step 10