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Math Help - Heaviside step function graph

  1. #1
    Member
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    Jul 2005
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    187

    Heaviside step function graph

    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
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    it's really easy using the definition of the step function we can deduce that:
    <br /> <br />
\begin{gathered}<br />
  1\left( {x + \pi } \right) = \left\{ \begin{gathered}<br />
  0\quad x <  - \pi  \hfill \\<br />
  1\quad x \geqslant  - \pi  \hfill \\ <br />
\end{gathered}  \right. \hfill \\<br />
  1\left( {x - \pi } \right) = \left\{ \begin{gathered}<br />
  0\quad x < \pi  \hfill \\<br />
  1\quad x \geqslant \pi  \hfill \\ <br />
\end{gathered}  \right. \hfill \\ <br />
\end{gathered} <br />

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

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