| home | contents | previous | next page | send comment | send link | add bookmark |

11. Graphs of polynomial functions

A polynomial function is a function in which the definition is a polynomial expression. All polynomials may be used as definitions of functions.

Univariate functions

A general univariate polynomial function is defined as:

f(x) = anxn + an-1xn-1 + an-2xn-2 + . . . + a2x2+ a1x + a0
Univariate functions may be graphed on the Cartesian plane. Univariate polynomial functions have these special names:
expression  name
f(x) = a  constant
f(x) = ax + b  linear
f(x) = ax2 + bx + c  quadratic
f(x) = ax3 + bx2 + cx + d  cubic
f(x) = ax4 + bx3 + cx2 + dx + e  quartic
f(x) = ax5 + bx4 + cx3 + dx2 + ex + f  quintic
Bivariate functions A general bivariate polynomial function is defined as:
f(x, y) = anmxnym + . . . + a11xy + a10x + a01y + a00
Bivariate functions can be graphed in three dimensions.

11.1. Linear functions
11.1.1. Slope and intercepts
11.1.2. Parallel and perpendicular lines
11.2. Quadratic Functions
11.2.1. Vertex form
11.3. Functions of higher order polynomials
11.3.1. Local extreme values
11.3.2. End behavior
11.4. Solved Problems


| home | contents | previous | next page | send comment | send link | add bookmark |

Copyright © 2005, Stephen R. Schmitt