1. Continuity

2. Definition
A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

3. Visually
A function is continuous if there are no breaks in the graph

4. Example:
At what points on the graph below is the function discontinuous?

5. Examples:
Where are each of these discontinuous? 1) 2) 3)

6. Three Types of Discontinuity
Removable Discontinuities
Infinite Discontinuities
Jump Discontinuities

7. Removable (Point) Discontinuity
Function redefined at a point

8. Infinite discontinuity

9. Jump Discontinuity

10. One-sided Continuity
A function is continuous from the right if and continuous from the left if

11. Continuous on a Interval
A function is continuous on its domain

12. Example:
Where is the function continuous?

13. Example
Where are the following continuous 1)