# Continuity of Functions

### Example 1

- Does a function
*f*that is bounded on [*a*,*b*] need to be continuous on [*a*,*b*]? Why or why not?

### Example 2

Does a function *f* that is continuous on an open interval (*a*,*b*) need to be bounded on that interval?

### Example 3

Does a function *f* that is discontinuous on a closed interval [*a*,*b*] need to be bounded on that interval?

### Example 4

Let . For each given function and interval, determine if we can use the Boundedness Theorem to conclude the function is bounded on that interval. If not, explain why not.

- [0,5]

- (0,5)

- (2,3)

- [0,1]

- [0,2)