1. ## Points of Discontinuity

Here is the graph: http://i.imgur.com/5a7wi.png

There is a removable discontinuity at x=-3 -- that is False because there is an open hole?
There is a removable discontinuity at x=-1 - is that false because there is an open hole and one closed?
There is a removable discontinuity at x=1 - Also false because one open and closed

Thank You for checking

2. ## Re: Points of Discontinuity

There is a removable discontinuity at x=-3 -- that is False because there is an open hole? the function is continuous at x = -3

There is a removable discontinuity at x=-1 - is that false because there is an open hole and one closed? there is an essential discontinuity at x = -1

There is a removable discontinuity at x=1 - Also false because one open and closed the discontinuity at x = 1 is removable ... redefining the function to be f(1) = 1 "removes" it

3. ## Re: Points of Discontinuity

Essential Discontinuities are not removable, correct?

And the discontinuity at x=3 is infinite right?

4. ## Re: Points of Discontinuity

Originally Posted by ritacame
Essential Discontinuities are not removable, correct? correct

And the discontinuity at x=3 is infinite right? yes
...

5. ## Re: Points of Discontinuity

There is a choice that looks like this:

What does that mean? Is it meaning that at negative infinity it DNE? Thats True because its an infinite discontinuity right?

Thanks

6. ## Re: Points of Discontinuity

the notation is stating the behavior of the function as x approaches 3 ... f(x) goes to -infinity, therefore the limit does not exist.