Checkpoint 3 Answers

1. This function is continuous on any interval because it has a derivative at every point of its domain.

2. This function is continuous on any interval of positive numbers — in spite of all the rapid wiggles near `x=0` — because it has a derivative at every point of its domain.

3. This function is continuous on any interval that does not include `x=0` because it has a derivative at every point of its domain.

4. This function is continuous on any interval that does not include `x = sqrt(2)`  or `x=-sqrt(2)`  because it has a derivative at every point of its domain.