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5-97.
  1. Sketch each of the following piecewise functions. Then, determine if the functions are continuous and differentiable over all reals. Homework Help ✎

To test if the function is continuous at the boundary point, use the three conditions of continuity:

2. f(a) exists.

To test if the function is differential at the boundary point, use the same three conditions on the derivative.

2. f '(a) exists. (Note, differentiability implies continuity.)

Notice that part (b) has two boundary points, so you will have to run these tests twice.