Heaviside step function graph

**totalnewbie** · May 17th 2008, 08:04 AM

I was wondering what the graph of the following function is:
f(x) = 1(x+pi) -2*1(x)+1(x-pi)
where 1(x)=0 if x < 0
and 1(x)=1 if x >= 0

**Peritus** · May 17th 2008, 09:15 AM

it's really easy using the definition of the step function we can deduce that:
$ \begin{gathered} 1\left( {x + \pi } \right) = \left\{ \begin{gathered} 0\quad x < - \pi \hfill \\ 1\quad x \geqslant - \pi \hfill \\ \end{gathered} \right. \hfill \\ 1\left( {x - \pi } \right) = \left\{ \begin{gathered} 0\quad x < \pi \hfill \\ 1\quad x \geqslant \pi \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} $

now all you have to do is combine the functions on each segment and you'll get:

$ f(x) = \left\{ \begin{gathered} 0\quad \;x \notin \left( { - \pi ,\pi } \right] \hfill \\ 1\quad \; - \pi \leqslant x < 0 \hfill \\ - 1\quad 0 \leqslant x < \pi \hfill \\ \end{gathered} \right.$

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