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USAGE IN ELEMENTARY MATHEMATICS

In elementary Algebra and Analytic Geometry , the term ''linear function'' is often used to mean a first degree Polynomial Function of one Variable . These functions are called "linear" because they are precisely the functions whose Graph in the Cartesian Coordinate Plane is a straight line.

Such a function can be written as

: f(x) = mx + b,

where m and b are Real Constant s and x is a real variable. The constant m is often called the Slope while b is the Y-intercept , which gives the point of intersection between the graph of the function and the y-axis. Changing m makes the line steeper or shallower, while changing b moves the line up or down.



Examples of functions whose graph is a line include the following:

  • f_{1}(x) = 2x+1

  • f_{2}(x) = x/2+1

  • f_{3}(x) = x/2-1


The graphs of these are shown in the image at right.


USAGE IN ADVANCED MATHEMATICS


In advanced mathematics, a ''linear function'' often means a Function that is a Linear Map , that is, a map between two Vector Space s that preserves vector addition and Scalar Multiplication .

A function f(x) = mx + b is a linear map if and only if b = 0. For other values of b this falls in the more general class of Affine Map s.


EXTERNAL LINKS

  • Linear function - Easy math

  • [http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/linearFunctions.html Linear Functions on Id Mind]