Consider the following piecewise function:
$$f(x) = \begin{cases} -x, & \mbox{if } x \leq 0 \\ x, & \mbox{if } x \ge 0 \end{cases}$$
I would like a technical term to refer to the point $x = 0$ which is the point at which the domains of the sub-functions intersect. For this specific example I could refer to it as the point at which the derivative $f'(x)$ is discontinuous however piecewise functions need not be discontinuous and so does a general term for this point exist? If not could you make a sensible recommendation on how to refer to it?