- Linear function
In
mathematics , the term linear function can refer to either of two different but related concepts.Analytic geometry
In
analytic geometry , the term "linear function" is sometimes used to mean a first degreepolynomial function of onevariable . These functions are called "linear" because they are precisely the functions whose graph in theCartesian coordinate plane is a straight line.Such a function can be written as
:
(called slope-intercept form), where and are real
constant s and is a real variable. The constant is often called theslope or gradient, while is they-intercept , which gives the point of intersection between the graph of the function and the -axis. Changing makes the line steeper or shallower, while changing moves the line up or down.Examples of functions whose graph is a line include the following:
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*The graphs of these are shown in the image at right.
Vector spaces
In advanced mathematics, a "linear function" often means a function that is a
linear map , that is, a map between twovector space s that preserves vector addition andscalar multiplication .For example, if and are represented as
coordinate vector s, then the linear functions are those functions that can be expressed as:, where M is a matrix.
A function is a linear map if and only if . For other values of this falls in the more general class of
affine map s.ee also
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Function (mathematics) External links
* [http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/linearFunctions.html Linear Functions on Id Mind]
* [http://www.mathopenref.com/linearexplorer.html Interactive tool to explore linear functions]
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