The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
An asymptote is a line a function will approach. The simplest varieties are either horizontal or vertical. A vertical asymptote occurs when the function at a certain value approaches infinity whether one comes at it from the positive or negative side. A horizontal asymptote occurs when the function approaches a certain value as it gets closer and closer to positive or negative infinity. The behavior of the function may oscillate around the asymptote, with gradually damping oscillations as it gets closer to infinity, or it may simply monotonically increase or decrease, depending on what type of function it is.
Functions which have a denominator of order one less than their numerator may have an oblique asymptote. An oblique asymptote is neither horizontal nor vertical, but rather is the portion of the function which approximates a straight line, appearing diagonal on the usual Cartesian axis. It clearly demonstrates the dominant terms in the function, those which determine the function's behavior far from the origin.
Asymptotic behavior can be useful in graphing a function. Its asymptotic behavior near zero and as the function approaches infinity can be combined to look very much like an exact graph of the function. Asymptotes can also be used in determining what approximations of a function may be appropriate. If the behavior of a function at a chosen limit is known, some series approximations may be ruled out for failure to match that behavior. While the asymptotic behavior of a function is never exact, it can nevertheless provide useful insight into how that function may be dealt with.