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

5-97.

Sketch each of the following piecewise-defined 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 3 Conditions of Continuity:

2. *f*(*a*) exists.

To test if the function is differential at the boundary point, use the same 3 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.