Continuity for piecewise-defined functions

[sean-fitzpatrick]

I just noticed that the textbook lacks an example relevant to this exercise group, which is a type of problem we frequently assess:

Given a piecewise-defined function, we want to know if it is continuous at the points where the "pieces" meet up.

So it becomes necessary to check:

1. lim_{x\to c^-}f(x)
2. lim_{x\to c^+}f(x)
3. f(c)

and confirm that all three are the same. The book moves quite quickly into determining intervals of continuity, without an example where we analyze continuity at a point.