00:01
Okay, so i have a piecewise function and then some questions about the limit at three for this function.
00:10
So i'm going to start off by graphing it.
00:14
And this is a piecewise function, as i said.
00:16
So it has different rules for different parts of its domain.
00:21
So i'm going to start with the part at the bottom, the x function, this guy, because that's where x is defined.
00:30
So for all my values greater than three, and including three, this graph will equal x.
00:39
So if my input is three, my output is three.
00:44
If my input is four, my output is four, my input is five, my output, i think you get the message.
00:52
So it's just this little linear function that starts at three.
00:56
Looks like that.
00:58
Now what about for values less than three? well for anything less than three, this top equation applies.
01:07
So what i do, so i can get really, really close to three, is i pretend for a moment i can plug in three.
01:14
I know i really can't because the bottom function is what's defined at three, but i pretend i can and i watch what happens.
01:21
So if i put in three into this function, i get four times three as a three.
01:26
12 minus 12, i get zero out.
01:29
So i go to three and i just put an open circle there.
01:34
Right? let me make that look a little bit better.
01:36
I'm going to put an open circle at three.
01:41
Now, this includes all those values less than negative three...