00:02
We have a whole sequence of problems that are, so some questions about this graph here that i've tried to reproduce from the book.
00:15
It's obviously piecewise, continuous.
00:18
It's not smooth because it looks like we have a corner there.
00:23
So it looks linear here, linear here, but, you know, with a constant y, and then some kind of, probably more like a, like a cubic.
00:33
Or a quartic function over here.
00:38
They don't tell us what these are.
00:41
We could, yeah, i think we have enough points.
00:46
Let's see here, we have one, two, three, four, five points.
00:50
We could figure out a quartic polynomial.
00:53
We probably want to find this slope here, so we could figure out a quintic polynomial that would have a zero slope here and go through through all these points if we wanted to, but that's not what we were asked.
01:08
So we're just asked a bunch of questions about this.
01:10
So i'm just gonna go through all of them in this one video, because they're all very much related, and they're all, you know, i have to do with this graph here.
01:20
So the first question is find f of zero and f of negative six.
01:24
Well, f of zero, that's when x equals zero.
01:28
So we come up here and we're at my, at three.
01:33
And then at negative 6 we're out here and so they've labeled this point here x is negative 6 then y is minus 3 now they ask us is f of 3 positive or negative so let's see here f of 3 is somewhere in this uh in this region here and so it's it's positive and it's probably you know, just again, they didn't label the point, but it looks like it's three for this whole region between zero and four.
02:11
And f of minus four, so minus three were at zero, minus five were at minus two.
02:23
So if this is indeed a line, then at minus four, we're at minus one.
02:27
And clearly, f of my, at f when x equals minus two, is clearly negative.
02:35
It's on, you know, it's to the left of here.
02:40
Now they ask us, let's see here.
02:45
For what values of x is f of x zero? well, f of x is y here.
02:51
So we have a zero here, a zero here, and a zero here.
02:56
So there's three points.
02:58
And they are when x is minus three, when x is six, and when x is 10, to those three points.
03:07
Then they ask us for what values of x is f greater than 0? well, we can see here that it's greater than 0 here and also here.
03:21
And i should probably say that this, i should probably change this to just assume that this doesn't get extended.
03:28
So we have, it's greater than equal to 10, less than equal to 11.
03:35
So from here to here, right, we have x equals minus 3 to 6.
03:42
So, and they said greater than.
03:46
All right, so i should have, i should just have greater than.
03:49
It's not equal to.
03:51
And then from here to here, you know, it goes from 10 to 11.
03:56
So over this region, the little region here, we also have positive values.
04:02
Then i asked for the, what is the domain? well, assuming that this doesn't continue on in any way, that this is just, you know, it's only defined over this region.
04:12
The domain goes from x equals minus 6 to x equals 11.
04:18
And they ask us for the range, and the range is, you know, the span of y values.
04:24
So it looks like the smallest y value we have is minus 3, and the largest value we have is 3.
04:32
So that's the range...