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In mathematics, the term linear function refers to two distinct but related notions:
A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. Its graph, when there is only one independent variable, is a horizontal line.
In this context, the other meaning (a linear map) may be referred to as a homogeneous linear function or a linear form. In the context of linear algebra, this meaning (polynomial functions of degree 0 or 1) is a special kind of affine map.
As a linear map
The integral of a function is a linear map from the vector space of integrable functions to the real numbers.