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 . This curve has both the -axis and the -axis as asymptotes.
As goes to infinity, the graph approaches the -axis from above; as goes to negative infinity, the graph approaches the -axis from below.
Similarly, as goes to infinity, the graph approaches the -axis from the right; as goes to negative infinity, the graph approaches the -axis from the left.
Diagonal asymptotes are also possible; for instance, the graph of has the line as an asymptote. (The -axis is also an asymptote.)