IN MATH: 1. n. a curve which is approached but never "reached" by a graph.

IN ENGLISH: 1. as defined above.

EX. 1: The graph of the reciprocal function, 1/x, has a vertical asymptote of x = 0 and a horizontal asymptote of y= 0. | |

EX. 2: This rational function also has vertical and horizontal asymptotes. The vertical asymptote is at x = 2 and there is a horizontal asymptote at y = 4. | |

EX. 3: This rational function also has a vertical asymptote at x = 2, but it has an oblique line asymptote at y = - x + 4. | |

EX. 4: This rational function also has a vertical asymptote at x = 2, but it has a quadratic asymptote at y = - x² + 4. |

APPLICATION: See list 230.

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