Asymptotic Graph Math

In mathematics an asymptote is a horizontal vertical or slanted line that a graph approaches but never touches. The word asymptote is derived from the greek ἀσύμπτωτος asumptōtos which means not falling together from ἀ priv. An asymptote is a line that a graph approaches without touching.

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Hardy and wright 1979 p.

Asymptotic graph math. In analytic geometry an asymptote ˈæsɪmptoʊt of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. No matter how far we go into infinity the line will not actually reach y 0 but will always get closer and closer. If a graph has a horizontal asymptote of y k then part of the graph approaches the line y k without touching it y is almost equal to k but y is never exactly equal to k. For example in the following graph of y 1 x y 1 x the line approaches the x axis y 0 but never touches it.

7 use the symbol to denote that one quantity is asymptotic to another. A line or curve a that is asymptotic to given curve c is called the asymptote of c. An asymptote is essentially a line that a graph approaches but does not intersect. σύν together.

Y 1 x y 1 x. In projective geometry and related contexts an asymptote of a curve is a line which is tangent to the curve at a point at infinity. If f phi then hardy and wright say that f and phi are of the same order of magnitude. The term asymptotic means approaching a value or curve arbitrarily closely i e as some sort of limit is taken.

The following graph has a horizontal asymptote of y 3.