So this is interesting, because the function at negative two is up here, and so if you really wanted to start at negative two, you would have to start here, and then jump immediately down as soon as you get slightly larger than negative two, and then keep going, but this is an open interval, so we're not actually concerned with what exactly happens at negative two. We're concerned what happens when we are all the numbers larger than negative two, so we would actually start right over here, and then we would go to one, and once again, based on the intuitive, I didn't have to pick up my pen idea, this function would be continuous over this interval. So what's an example of an interval where the function would not be continuous? Well, think about the interval from, well, this is a pretty straightforward one, the open interval from three to five. The function is here when x is equal to three, but if we wanted to get to five, it looks like we're asymptoting, it looks like we're asymptoting up towards infinity, and we just keep on going for a very long time, and then we would have to pick up our pencil and jump over, and then we would come back down right over here, and so here, we are not continuous over that interval. So now let's think about the more, the slightly more involved interval, the slightly more involved case is when you have a closed interval. F is continuous over the closed interval from a to b, so this includes not just the points between a and b, but the endpoints as well, if and only if f is continuous over the open interval and the one-sided limits, let me write this, and the limit as x approaches a from the right of f of x is equal to f of a, and the limit as x approaches b from the left of f of x is equal to f of b.