Sketch each of the following piecewise-defined functions. Then, determine if the functions are continuous and differentiable over all reals.
To test if the function is continuous at the boundary point, use the 3 Conditions of Continuity:
To test if the function is differential at the boundary point, use the same 3 conditions on the derivative.
Notice that part (b) has two boundary points, so you will have to run these tests twice.