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Truncus (mathematics)
In analytic geometry, a truncus is a curve in the Cartesian plane consisting of all points (''x'',''y'') satisfying an equation of the form
where ''a'', ''b'', and ''c'' are given constants. The two asymptotes of a truncus are parallel to the coordinate axes. The basic truncus y = 1 / ''x''2 has asymptotes at ''x'' = 0 and ''y'' = 0, and every other truncus can be obtained from this one through a combination of translations and dilations.
For the general truncus form above, the constant ''a'' dilates the graph by a factor of ''a'' from the ''x''-axis; that is, the graph is stretched vertically when ''a'' > 1 and compressed vertically when 0 < ''a'' < 1. When ''a'' < 0 the graph is reflected in the ''x''-axis as well as being stretched vertically. The constant ''b'' translates the graph horizontally left ''b'' units when ''b'' > 0, or right when ''b'' < 0. The constant ''c'' translates the graph vertically up ''c'' units when ''c'' > 0 or down when ''c'' < 0.
The asymptotes of a truncus are found at ''x'' = ''b'' (for the vertical asymptote) and ''y'' = ''c'' (for the horizontal asymptote).
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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