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Asymptote

A linethat 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 distancebetween the curve and the asymptote tends to zeroas they head to infinity (or !infinity)

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"orizontal Asymptotes

#t is a "orizontal Asymptote when:

as $ goes to infinity (or !infinity) the curve approaches some constant value b

%ertical Asymptotes

#t is a %ertical Asymptote when:

as $ approaches some constant value c(from the left or right) then the curve goes towards

infinity (or !infinity)

&blique Asymptotes

#t is an &blique Asymptote when:

as $ goes to infinity (or !infinity)then the curve goes towards a liney=mx+b

(note: m is not zero as that is a "orizontal Asymptote)

'$ample: ($*$)+($)

Thegraph of (x2-3x)/(2x-2)has:

A vertical asymptote at x=1

An oblique asymptote: y=x/2-1

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