In mathematics, a piecewise linear function is a piecewise-defined function whose pieces are linear.

The function defined by:

is piecewise linear with four pieces. (The graph of this function is shown to the right.) Since the graph of a linear function is a line, the graph of a piecewise linear function consists of line segments and rays. If the function is continuous, the graph will be a polygonal curve. In simple piece wise linear function means line fitting with reference to different points.

Other examples of piecewise linear functions include the absolute value function, the square wave, the sawtooth function, and the floor function.

The notion of a piecewise linear function makes sense in several different contexts. Piecewise linear functions may be defined on n-dimensional Euclidean space, or more generally any vector space or affine space, as well as on piecewise linear manifolds, simplicial complexes, and so forth. In each case, the function may be real-valued, or it may take values from a vector space, an affine space, a piecewise-linear manifold, or a simplicial complex. (In these contexts, the term “linear” does not refer solely to linear transformations, but to more general affine linear functions.)

In mathematics, the term linear function can refer to either of two different but related concepts:

In analytic geometry, the term linear function is sometimes used to mean a first-degree polynomial function of one variable. These functions are known as "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

(called slope-intercept form), where Failed to parse (Missing texvc executable; please see math/README to configure.): m

-axis. Changing Failed to parse (Missing texvc executable; please see math/README to configure.): m

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

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

In advanced mathematics, a linear function means a function that is a linear map, that is, a map between two vector spaces that preserves vector addition and scalar multiplication.

For example, if Failed to parse (Missing texvc executable; please see math/README to configure.): x

Piecewise linear, often abbreviated to PL, may refer to: