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In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity.

www.mathsisfun.com/algebra/asymptote.html

An asymptote is a line that a curve approaches, as it heads towards infinity: ... approach from any side (such as from above or below for a horizontal asymptote) ,.

mathworld.wolfram.com/Asymptote.html

An asymptote is a line or curve that approaches a given curve arbitrarily closely, ... Wolfram Web Resource. http://mathworld.wolfram.com/Asymptote.html ...

www.khanacademy.org/questions/what-are-asymptotes/kafb_4768525

An asymptote is a line that the curve never touches but approaches. like say the curve y=1/x will never touch the line x=0(y-axis) nor the y=0(x-axis). so the ...

www.freemathhelp.com/finding-horizontal-asymptotes.html

Horizontal asymptotes are approached by the curve of a function as x goes towards infinity. Calculate their value algebraically and see graphical examples with ...

www.freemathhelp.com/asymptotes.html

Asymptotes are invisible lines which are graphed function will approach very closely but not ever touch. This lesson covers vertical and horizontal asymptotes ...

www.purplemath.com/modules/asymtote.htm

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. (They can also arise in other contexts, such as ...