en.wikipedia.org/wiki/Asymptote

In analytic geometry, an **asymptote** of a curve is a line such that the distance
between the curve and the line approaches zero as one or both of the x or y
coordinates tends to infinity. Some sources include the requirement that the curve
may not cross the line infinitely often, but this is unusual for modern authors. In
some ...

www.mathsisfun.com/algebra/asymptote.html

**Asymptote**. An **asymptote** is a line that a curve approaches, as it heads towards
infinity: **Asymptote**. Types. There are three types: horizontal, vertical and oblique:
**Asymptote** Types. The direction can also be negative: **asymptote** negative infinity.
The curve can approach from any side (such as from above or below for a ...

www.khanacademy.org/questions/what-are-asymptotes/kafb_4768525

**Asymptotes** are more like lines which a function (graph) never reaches (though it
usually comes close). If you consider the function f(x) = 3/x, obviously x can never
be 0, because then f(x) would equal 3/0, which is undefined. Therefore, the
**asymptote** is a line. The equation of the **asymptote** (line) would be x = 3, a vertical
line ...

mathworld.wolfram.com/Asymptote.html

**Asymptote**. DOWNLOAD Mathematica Notebook · EXPLORE THIS TOPIC IN the
MathWorld Classroom **Asymptote**. An **asymptote** is a line or curve that
approaches a given curve arbitrarily closely, as illustrated in the above diagram.
**AsymptotesOneOverX**. The plot above shows 1/x , which has a vertical **asymptote**
at x=0 ...

www.purplemath.com/modules/asymtote2.htm

Uses worked examples to explain how to find horizontal **asymptotes**. Explains
how functions and their graphs get "close" to horizontal **asymptotes**, and shows
how to use exponents on the numerators and denominators of rational functions
to quickly and easily determine horizontal **asymptotes**.

www.purplemath.com/modules/asymtote4.htm

Purplemath. So far, we've dealt with each type of **asymptote** separately, kind of
like your textbook probably does, giving one section in the chapter to each type.
But on the test, the questions won't specify which type you need to find. In general
, you will be given a rational (fractional) function, and you will need to find the ...

www.purplemath.com/modules/asymtote.htm

Uses worked examples to demonstrate how to find vertical **asymptotes**. Stresses
the relation between vertical **asymptotes** and the domain of the function.

www.softschools.com/math/calculus/finding_horizontal_asymptotes_of_rational_functions

Remember that an **asymptote** is a line that the graph of a function approaches but
never touches. Rational functions contain **asymptotes**, as seen in this example: In
this example, there is a vertical **asymptote** at x = 3 and a horizontal **asymptote** at y
= 1. The curves approach these **asymptotes** but never cross them.