Examples Piecewise linear function

a continuous piecewise linear function

the function defined by:

f
(
x
)
=


{



−
x
−
3



if 

x
≤
−
3




x
+
3



if 

−
3
<
x
<
0




−
2
x
+
3



if 

0
≤
x
<
3




0.5
x
−
4.5



if 

x
≥
3








{\displaystyle 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}}}

is piecewise linear 4 pieces. (the graph of function shown right.) since graph of linear function line, graph of piecewise linear function consists of line segments , rays.

other examples of piecewise linear functions include absolute value function, square wave, sawtooth function, , floor function.