Editing Piecewise linear function (section)

==Examples==
[[Image:Piecewise linear function.svg|right|thumb|A continuous piecewise linear function]]
The function defined by
: <math>f(x) =
\begin{cases}
 -x - 3     & \text{if }x \leq -3 \\
 x + 3      & \text{if }-3 < x < 0 \\
 -2x + 3    & \text{if }0 \leq x < 3 \\
 0.5x - 4.5 & \text{if }x \geq 3
\end{cases}</math>
is piecewise linear with four pieces. The graph of this function is shown to the right. Since the graph of an affine(*) function is a [[line (geometry)|line]], the graph of a piecewise linear function consists of [[line segment]]s and [[ray (mathematics)|rays]]. The ''x'' values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots. As in many applications, this function is also continuous. The graph of a continuous piecewise linear function on a compact interval is a [[polygonal chain]].

(*) A [[linear map|linear function]] satisfies by definition <math> f(\lambda x) = \lambda f(x) </math> and therefore in particular <math> f(0) = 0 </math>; functions whose graph is a straight line are ''[[affine function|affine]]'' rather than ''linear''.

There are other examples of piecewise linear functions:
* [[Absolute value]]<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Piecewise Function|url=https://mathworld.wolfram.com/PiecewiseFunction.html|access-date=2020-08-24|website=mathworld.wolfram.com|language=en}}</ref>
* [[sawtooth wave|Sawtooth function]]
* [[Floor function]]
* [[Step function]], a function composed of constant sub-functions, so also called a piecewise constant function
** [[Boxcar function]],
** [[Heaviside step function]]<ref name=":0" />
** [[Sign function]]
* [[Triangular function]]