1. Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.

2. Definition f(x) is continuous at x=c if and only if: 1. f (c) is defined …and 2. exists …and 3.

3. Definition f(x) is continuous on the open interval ( a,b ) if and only if f(x) is continuous at every point in the interval.

4. Definition f(x) is continuous on the closed interval [ a,b ] iff it is continuous on ( a,b ) and continuous from the right at a and continuous from the left at b.

5. Example a b f(x) f(x) is continuous from the right at a

6. Example a b f(x) f(x) is not continuous from the left at b f(x) is continuous on [ a,b )

7. Example Find the intervals at which f(x) is continuous and the points at which f(x) is discontinuous 1234 1 2

8. Examples “Continuous” Functions i.e. they are continuous (-, + )

9. Examples Discontinuous Functions Removable discontinuity Jump Discontinuity (non- removable) Infinite discontinuity (non- removable)