A023othergraphs

Graphs of Other Algebraic Functions

 * Rational Functions **

Any function in the form: math . \qquad \qquad y = \dfrac{ g(x) }{ f(x) } \qquad. math
 * where f(x) and g(x) are polynomials

will have a maximal or implied domain of R excluding the values where f(x) = 0

The simplest rational function is the hyperbola with vertical and horizontal asymptotes (rectangular hyperbola)

math . \qquad \text{The Standard Hyperbola: } y = \dfrac{1}{x} \qquad. math

Another common rational function is the truncus with vertical and horizontal asymptotes (truncus)
 * The positive truncus looks like the trunk of a tree.

math . \qquad \text{The Standard Truncus: } y = \dfrac{1}{x^2} \qquad. math


 * Square Root and Cube Root Functions **

The square root function has the rule math . \qquad \text{The Standard Square Root Function: } y = x^\dfrac{1}{2} \qquad \text{or } y = \sqrt{x} \qquad. math

The cube root function has the rule math . \qquad \text{The Standard Cube Root Function: } y = x^\dfrac{1}{3} \qquad \text{or } y = \sqrt[3]{x} \qquad. math

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