Asymptotes

The asymptotes are straight lines on a graph that a function approaches indefinitely.

Horizontal Asymptotes

Example

Calculate the horizontal asymptote of the function:

Function

Horizontal Asymptote

Vertical Asymptotes

Vertical Asymptotes

K are the points outside the domain of the function (in the rational functions).

Example

Calculate the horizontal and vertical asymptotes of the function:

Function

Vertical Asymptote

Vertical Asymptote

Asymptotes

Oblique Asymptotes

Function

Oblique Asymptote

The oblique asymptotes will only be found when there are not horizontal asymptotes.

Example

Calculate the asymptotes of the function:

Function

Horizontal Asymptotes

Asymptote

Asintotas

Vertical Asymptotes

Asymptote

Asintotas

Oblique Asymptotes

Asymptote

Asymptote

Asymptote

Oblique Asymptote