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# 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)

 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

 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

 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 to -infinity) then the curve goes towards a line defined by y=mx+b (note: m is not zero as that would be horizontal).

### Example: (x2-3x)/(2x-2)

 The graph of (x2-3x)/(2x-2) has: A vertical asymptote at x=1 An oblique asymptote: y=x/2-1