Linear Function
In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A linear function in one variable x therefore has the form
| f(x)=ax+b, |
(1)
|
while a linear function in n variables has the form
| f(x_1,...,x_n)=b+a_1x_1+...+a_nx_n. |
(2)
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In linear algebra and functional analysis, a linear function is a function f which satisfies the linearity conditions
| f(x+y)=f(x)+f(y) |
(3)
|
and
| f(alphax)=alphaf(x) |
(4)
|
See also
Bilinear Function, Function, Line, Linear Functional, Piecewise Linear Function, Polynomial Function, Vector Space Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Linear Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinearFunction.html