Vertical Asymptotes - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

Home : Support : Online Help : Math Apps : Graphing : Basic : Vertical Asymptotes

Vertical Asymptotes

Main Concept

An asymptote is a line that the graph of a function approaches as either x or y approaches infinity. There are three types of asymptotes: vertical, horizontal and oblique.

Vertical Asymptotes

Vertical Asymptote

A vertical asymptote is a vertical line, , that has the property that either:

 

1.

2.

 

That is, as  approaches  from either the positive or negative side, the function approaches infinity.

 

Vertical asymptotes occur at the values where a rational function has a denominator of 0. The function is undefined at these points.

Horizontal Asymptotes

Horizontal Asymptote

A horizontal asymptote is a horizontal line, , that has the property that either:

 

1.

2.

 

Horizontal asymptotes occur when the numerator of a rational function has degree less than or equal to the degree of the denominator. If the denominator has degree , the horizontal asymptote can be calculated by dividing the coefficient of the -th term of the numerator (it may be 0 if the numerator has a smaller degree) by the coefficient of the -th term of the denominator.

Oblique Asymptotes

Oblique Asymptote

An oblique or slant asymptote is an asymptote along a line , where . Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator.

 

Click or drag to place up to 5 points through which a curve (blue) will be drawn. The -intercepts (green), the reciprocal of the curve (black) and any vertical asymptotes of the reciprocal (magenta) will also be shown.

 

 

 

 

 

 

 

 

 

More MathApps

MathApps/Graphing

 


Download Help Document