# Piecewise Continuous Function

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A Piecewise Continuous Function is a continuous function that is a piecewise function.

**See:**Fourier Transform.

## References

### 2016

- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Piecewise#Continuity Retrieved:2016-1-3.
- A piecewise function is continuous on a given interval if the following conditions are met:
- it is defined throughout that interval
- its constituent functions are continuous on that interval
- there is no discontinuity at each endpoint of the subdomains within that interval.

- The pictured function, for example, is piecewise continuous throughout its subdomains, but is not continuous on the entire domain. The pictured function contains a jump discontinuity at [math]\displaystyle{ x_0 }[/math] .

- A piecewise function is continuous on a given interval if the following conditions are met: