00:01
All right, so in this problem, we've got to take some limits.
00:04
It looks like we have a piecewise function.
00:07
Let's see if i can write it.
00:09
So h of x equals, and then we have x up here at the top, and when x is less than zero, and then we have x squared for zero to two.
00:33
I don't know where the closed circle or open circle is supposed to be.
00:39
So 0 less than x, less than 8, oh, i think it's less than or equal to 2, like that.
00:48
And then making a guess, and then 8 minus x, i believe, i can't really see, for x is greater than x is greater than two all right and i'm going to i'm going to put a line under this just to uh just to one of them has to be equal okay so to graph this thing here's how you graph it uh you so we need an x y axis so here's my y axis here's my x axis one, two, three, four, five.
01:47
Okay, so when x is less than or equal to zero, we're going to be using this top function right here.
01:56
Y equals x.
01:57
That's what we're graphing.
01:58
So i'm going to get a closed circle here, and then when i go backwards, because i got to go less than zero, when i put negative one in, i get negative one.
02:13
And when i put negative two in, i get negative two.
02:15
And negative 3, i get negative 3.
02:19
And so we're basically going to get this line that stops at this closed circle and goes to the left.
02:28
Keeps going.
02:29
It's the top equation.
02:31
Now, when we graph x squared, let me use a different color.
02:36
When i put zero in for x, i get zero, but it's going to be an open circle right there.
02:42
Okay? so for the x squared, it's open because the inequality is not a lot.
02:47
Underlined.
02:48
When i put one in, i get one.
02:50
When i put two and i get four.
02:53
Numbers here.
02:55
One, two, three, four, five.
03:01
Two, i get one, two, three, four.
03:03
I'm up here.
03:04
So, so this is the, it's just a little piece of the parabola.
03:08
It's a closed circle on the right side because i, i don't know if it's supposed to be less than or equal to two.
03:14
I'm just guessing because i couldn't read it.
03:16
So there you go.
03:17
Now, for greater than two, we're using this last equation, 8 minus x.
03:23
Now, it hits the y -axis up at 8, but that's not in the interval.
03:27
What i like to do is, like, when i put 2 in for x, 8 minus 2 is 6, so i'm up here at 6, which is with an open circle, and then when i put 3 in, i'm at 5, so it's going to be about right here.
03:44
When i put four in, i'm at four.
03:48
So i'm going to get this line, this green line going like this.
03:54
And there's an open circle because see how the inequality right there is not underlined.
03:58
That's why it's an open circle.
04:00
Okay...