00:01
Here, we're asked to sketch the graph of a function that satisfies all of these requirements.
00:06
So what i'm going to do is first start off by looking at what regions are we discussing.
00:10
So that means basically i'm looking at x equals negative infinity.
00:14
That's the smallest point, negative infinity.
00:18
We also care about negative three.
00:21
We also care about two and five and infinity.
00:26
So i'm going to kind of think of those points in that order.
00:29
So let's just think about what does it look at like? from negative infinity to negative in 3.
00:35
Negative 3.
00:36
So we go to negative infinity for that as x goes to negative infinity.
00:43
And then we have an asymptote at negative 3.
00:45
So i'm going to go ahead and draw an asymptote at negative 3.
00:50
And as it goes to that an asymptote, it goes to infinity.
00:55
So it needs to approach infinity.
00:57
And also as it goes back to negative infinity, it needs to go back up again.
01:01
So it's going to come down and come like that.
01:05
Where it goes up to infinity.
01:06
So now we've satisfied a and d.
01:11
Now let's look at the next region from negative 3 to 2.
01:17
So the limit as x approaches negative 3 is infinity on either side.
01:21
So it's going to go up to infinity here.
01:24
And then as i look at 2 from the left, that's going to matter here.
01:30
It goes to negative infinity...