asymptote
Sign in to saveright|thumb|250px|The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) right|thumb|250px|A curve intersecting an asymptote infinitely many times
AI overview
An asymptote is a line that a curve approaches more and more closely as it extends, without actually reaching it—whether the line is horizontal, vertical, or slanted. Asymptotes matter because they help us understand the long-term behavior of mathematical functions and curves, making it easier to sketch graphs and predict how systems behave at extreme values.
AI-generated from the Wikipedia summary — may contain errors.
Article
19 sectionsContents
- Introduction
- Asymptotes of functions
- Vertical asymptotes
- Horizontal asymptotes
- Oblique asymptotes
- Elementary methods for identifying asymptotes
- General computation of oblique asymptotes for functions
- Asymptotes for rational functions
- Oblique asymptotes of rational functions
- Transformations of known functions
- General definition
- Generalizations and related concepts
- Curvilinear asymptotes
- Asymptotes and curve sketching
- Algebraic curves
- Asymptotic cone
- See also
- References
- External links
right|thumb|250px|The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) right|thumb|250px|A curve intersecting an asymptote infinitely many times
In analytic geometry, an asymptote () of a curve is a straight 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. 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.