Which of the following is true for ALL piecewise functions?

The limit always exists at a boundary point.

The limit never exists at a boundary point.

If each piece is a polynomial then the limit exists at every point.

If each piece is a polynomial then the limit exists at every point which is not a boundary point.

None of the above is ever true.

None of the above is always true, but all of them may be true for some values of x.