# Give an example of Piecewise-Defined Functions?

Give an example of Piecewise-Defined Functions?
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Step 1
By a piecewise defined function, a function of the form
$f\left(x\right)=\left\{\begin{array}{cc}g\left(x\right)& \phantom{\rule{1em}{0ex}}\text{if}\phantom{\rule{1em}{0ex}}x\in A\\ h\left(x\right)& \phantom{\rule{1em}{0ex}}\text{if}\phantom{\rule{1em}{0ex}}x\in A\end{array}\right\}$
Where g(x) h(x)
Are any fixed function.
Step 2
For example:
$f\left(x\right)=\left\{\begin{array}{cc}1& \phantom{\rule{1em}{0ex}}\text{if}\phantom{\rule{1em}{0ex}}x\ge 0\\ 0& \phantom{\rule{1em}{0ex}}\text{if}\phantom{\rule{1em}{0ex}}x<0\end{array}\right\}$
Called unit step function, is an example for piecewise defined function and also has many applications in signal processing systems.