linear function
A "linear function" is a fundamental concept in mathematics, often used to model relationships where a constant change in one variable results in a proportional change in another.
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Definition
B2Algebra
(academic, technical)A function that can be written in the form f(x) = mx + b, where m and b are constants, and its graph is a straight line.
Example
- The equation f(x) = 2x + 3 represents a linear function.
C1Vector Space
(technical, advanced)A function that preserves vector addition and scalar multiplication, meaning f(ax + by) = af(x) + bf(y) for all scalars a, b and vectors x, y.
Example
- In linear algebra, the transformation T(x) = 3x is a linear function.
Similar
Terms that have similar or relatively close meanings to "linear function":
linear dependencepiecewise linearline graphlinear algebraplain linemonotone functiongreen linerectified linear unitloop line