A line which approaches nearer to some curve than assignable distance, but, though infinitely extended, would never meet it. Asymptotes may be straight lines or curves. A rectilinear asymptote may be conceived as a tangent to the curve at an infinite distance.

On a graph, a curve which is approached but never reached.

a straight line to which a curve continuously draws nearer without ever touching it.

a straight line that is the limiting value of a curve; can be considered as tangent at infinity; "the asymptote of the curve"

a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram

a line that a graph approaches, but doesn't ever reach, as its x - or y - values become very large or very small

a line that a graph approaches but never intersects

a line which the graph gets very close to, but does not touch

a line whose distance to a given curve tends to zero and may or may not intersect its associated curve

an infinitely long straight line which sort of acts like a boundary

a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line

a straight or curved line which a curve will approach arbitrarily closely, but never touch

a way of describing how a graph looks when an infinity is approached

A line related to a given curve such that the distance from the line to a point on the curve approaches zero as the distance of the point from an origin increases without bound.

If the graph of a function approaches a horizontal line or a vertical line, we call the line an asymptote.

Straight lines that have the property of becoming and staying arbitrarily close to the curve as the distance from the origin increases to infinity. For example, the -axis is the only asymptote to the graph of sin()/.

A line that is considered to be the limit to a curve. As the curve approaches the asymptote, the distance separating the curve and the asymptote continues to decrease, but the curve never actually intersects the asymptote.

An asymptote is a straight line that defines the limits of a curve (such as a hyperbola). In the picture above, the dashed lines are asymptotes of the hyperbola.

An asymptote is a straight line or curve A to which another curve B (the one being studied) approaches closer and closer as one moves along it. As one moves along B, the space between it and the asymptote A becomes smaller and smaller, and can in fact be made as small as one could wish by going far enough along. A curve may or may not touch or cross its asymptote.