# Continuity of Functions

# Continuity on Closed and Half-Closed Intervals Exercises

### Example 1

What must be true for a function to be continuous on an interval of the form (*a*,*b*]?

### Example 2

What must be true for a function to be continuous on an interval of the form [*a*,*b*]?

### Example 3

Determine if *f* is continuous on each of the following intervals.

- [
*a*,*b*] - [
*a*,*b*) - (
*a*,*b*] - (
*a*,*b*)

### Example 4

Determine if *f* is continuous on each of the following intervals.

- [
*a*,*b*]

- [
*a*,*b*)

- (
*a*,*b*]

- (a,
*b*)

### Example 5

Determine if *f* is continuous on each of the following intervals.

- [
*a*,*b*] - [
*a*,*b*) - (
*a*,*b*] - (
*a*,*b*)

### Example 6

Determine if the function

[-1,0] [-1,0) (-1,0] (-1,0) [0,1] [0,1) (0,1] (0,1)

### Example 7

Determine if the function

is continuous on each of the following intervals.

- [0,1]
- [0,1)
- (0,1]
- (0,1)
- [1,5]
- [1,5)
- (1,5]
- (1,5)