Asymptote

An asymptote is a line that a curve approaches, as it heads towards infinity:

Types

There are three types: horizontal, vertical and oblique:

The direction can also be negative:

The curve can approach from any side (such as from above or below for a horizontal asymptote),

or may actually cross over (possibly many times), and even move away and back again.

The important point is that:

Horizontal Asymptotes

It is a Horizontal Asymptote when:

as x goes to infinity (or −infinity) the curve approaches some constant value b

Vertical Asymptotes

It is a Vertical Asymptote when:

as x approaches some constant value c (from the left or right) then the curve goes towards infinity (or −infinity).

Oblique Asymptotes

It is an Oblique Asymptote when:

as x goes to infinity (or −infinity) then the curve goes towards a line y=mx+b

(note: m is not zero as that is a Horizontal Asymptote).

These questions will only make sense when you know Rational Expressions: