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Asymptotes

An asymptote to a curve is a straight line which the curve approaches without crossing it. If we go sufficiently far along the line, the curve becomes arbitrarily close.

A simple example is the graph of y = 1 x . This curve has both the x -axis and the y -axis as asymptotes.

Math diagram

As x goes to infinity, the graph approaches the x -axis from above; as x goes to negative infinity, the graph approaches the x -axis from below.

Similarly, as y goes to infinity, the graph approaches the y -axis from the right; as y goes to negative infinity, the graph approaches the y -axis from the left.

Diagonal asymptotes are also possible; for instance, the graph of y = 1 x   + x has the line y = x as an asymptote. (The y -axis is also an asymptote.)

Math diagram

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