### Home > CALC > Chapter 5 > Lesson 5.2.4 > Problem 5-97

5-97.

Sketch each of the following piecewise 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 three conditions of continuity: exists.

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

*exists. (Note, differentiability implies continuity.)*

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