Piecewise Linear Function
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A Piecewise Linear Function is a piecewise function that is composed of Linear Functions.
- Example(s):
- [math]\displaystyle{ f(x) = \begin{cases} -x-3 & \text{if }x \leq -3 \\ x+3 & \text{if }-3 \lt x \lt 0 \\ -2x+3 & \text{if }0 \leq x \lt 3 \\ x-6 & \text{if }x \geq 3 \end{cases} }[/math]
- Counter-Example(s):
- See: Constant Piecewise Function, Sparse Piecewise Linear Algorithm.
References
2012
- http://en.wikipedia.org/wiki/Piecewise_linear_function
- In mathematics, a piecewise linear function is a function composed of straight-line sections. It is a piecewise-defined function whose pieces are linear.
If the function is continuous, the graph will be a polygonal curve.
- In mathematics, a piecewise linear function is a function composed of straight-line sections. It is a piecewise-defined function whose pieces are linear.
- http://en.wikipedia.org/wiki/Piecewise_linear_function#Examples
- The function defined by: :[math]\displaystyle{ f(x) = \begin{cases} -x-3 & \text{if }x \leq -3 \\ x+3 & \text{if }-3 \lt x \lt 0 \\ -2x+3 & \text{if }0 \leq x \lt 3 \\ x-6 & \text{if }x \geq 3
\end{cases} }[/math] is piecewise linear with four pieces. Since the graph of a linear function is a line, the graph of a piecewise linear function consists of line segments and rays.
Other examples of piecewise linear functions include the absolute value function, the square wave, the sawtooth function, and the floor function.
- The function defined by: :[math]\displaystyle{ f(x) = \begin{cases} -x-3 & \text{if }x \leq -3 \\ x+3 & \text{if }-3 \lt x \lt 0 \\ -2x+3 & \text{if }0 \leq x \lt 3 \\ x-6 & \text{if }x \geq 3
\end{cases} }[/math] is piecewise linear with four pieces. Since the graph of a linear function is a line, the graph of a piecewise linear function consists of line segments and rays.