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 ${\displaystyle x=0}$ — because it has a derivative at every point of its domain.

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

4. This function is continuous on any interval that does not include ${\displaystyle x=\sqrt{2}}$  or ${\displaystyle x=-\sqrt{2}}$  because it has a derivative at every point of its domain.