**Vertical asymptote.**
A line is called a *vertical asymptote*
for if

or

as approaches from either the left or the right.
A linear rational function (1) has
the vertical asymptote
(assuming
).
In general, when and in (2), the line becomes a vertical asymptote for (2). If and , the point can be considered as a ``hole.''

**Horizontal asymptote.**
A line is called a *horizontal asymptote*
for if

as
(or
).

A linear rational function (1) has
the horizontal asymptote .
In general,

- if in (2),
has the horizontal asymptote .
- If ,
has the horizontal asymptote
with the respective leading coefficients
and of and .
- If , has no horizontal asymptote.

**Oblique asymptote.**
A line
is called a *oblique asymptote*
if can be expressed in the form

Department of Mathematics