What's the difference between continuous and piecewise continuous functions? A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. 
I was looking at the image of a piecewise continuous function on the following page: http://tutorial.math.lamar.edu/Classes/DE/LaplaceDefinition.aspx 
But the image of the function they've presented isn't continuous. As such, I'm confused by what a piecewise continuous function is and the difference between it and a normal continuous function.
I'd appreciate it if someone could explain the difference between a continuous function and a piecewise continuous function. Also, please reference the image of the piecewise continuous function presented on this page http://tutorial.math.lamar.edu/Classes/DE/LaplaceDefinition.aspx .
Thank you.

A piecewise continuous function doesn't have to be continuous at finitely many points in a finite interval, so long as you can split the function into subintervals such that each interval is continuous.
A nice piecewise continuous function is the floor function:

The function itself is not continuous, but each little segment is in itself continuous.
