linear function
In mathematics, the term linear function can refer to either of two different but related concepts.
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
Such a function can be written as
- f(x) = mx + b
(called slope-intercept form), where m and b are
real constants and x
is a real variable. The constant m is often called the
Examples of functions whose graph is a line include the following:
- f1(x) = 2x + 1
- f2(x) = x / 2 + 1
- f3(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
spaces that preserves vector addition and
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
External links
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