Asymptote
A line that a curve approaches as it heads towards infinity:
Types
There are three types: horizontal, vertical and oblique:
The curve can approach from any side (such as from above or below for a horizontal asymptote)
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And 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
Horizontal Asymptotes
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It is a Horizontal Asymptote when:
as x goes to infinity (or to -infinity) then the curve approaches some fixed constant value "b" |
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) |
Oblique Asymptotes
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It is an Oblique Asymptote when:
as x goes to infinity (or to -infinity) then the curve goes towards a line defined by y=mx+b (note: m is not zero as that would be horizontal). |
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