Asymptote
A line that a curve approaches, as it heads towards infinity:
Types
There are three types: horizontal, vertical and oblique:
It can be in a negative direction,
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:
The distance between the curve and the asymptote tends to zero as they head to infinity (or −infinity)
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). 
Example: (x^{2}3x)/(2x2)
The graph of (x^{2}3x)/(2x2) has:

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