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Asymptotes
Anasymptoteto 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. This curve has both the-axis and the-axis as asymptotes.
Asgoes to infinity, the graph approaches the-axis from above; asgoes to negative infinity, the graph approaches the-axis from below.
Similarly, asgoes to infinity, the graph approaches the-axis from the right; asgoes to negative infinity, the graph approaches the-axis from the left.
Diagonal asymptotes are also possible; for instance, the graph ofhas the lineas an asymptote. (The-axis is also an asymptote.)