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
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It is a Horizontal Asymptote when:
as x goes to infinity (or −infinity) the curve approaches some constant value b
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Vertical Asymptotes
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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).
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Oblique Asymptotes
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It is an Oblique Asymptote when:
as x goes to infinity (or −infinity)then the curve goes towards a liney=mx+b
(note: m is not zero as that is a Horizontal Asymptote).
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