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If part of a graph is unbounded and there is a fixed straight line l such that the distance from a point P on the graph to l tends to 0 as OP → ∞, where O is the origin, then l is an asymptote to the curve. Alternatively, it is the limiting position of the tangent to the graph at P, as OP → ∞. For example, the asymptotes of the graph of are y=2x+3 and x=2.

Asymptote. The dotted lines are the asymptotes (vertical, x=2; oblique, y=2x+3) of the graph y=2x+3- 1/x-2.

Subjects: Probability and Statistics.

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