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)

Answer

Answer. If we graph the function, we see this:

Although *f* is discontinuous at 1 when we look at the whole graph, *f*(1) agrees with its right-sided limit (that is, ). This means if *x* = 1 is the left endpoint of an interval, *f* can be continuous on that interval.

- [0,1] - No, because
*.* - [0,1) - Yes, because x = 1 is not included in this interval
- (0,1] - No, because .
- (0,1) - Yes, because x = 1 is not included in this interval
- [1,5] - Yes, because
*f* is continuous on (1,5] and - [1,5) - Yes, because
*f* is continuous on (1,5) and - (1,5] - Yes
- (1,5) - Yes