00:01
Okay, we're doing some graphing and analyzing, so this is going to be fun.
00:06
So let's go ahead and look at the first function a, x times e to the x power.
00:11
So here is x times e to the x power in red.
00:16
It looks kind of strange, but we'll work with it.
00:20
The domain is everything it looks like, negative infinity to infinity.
00:30
And the range, well, the lowest y value that we can see in its next streama, that's why desmos is pointing it out.
00:38
So the range is going to be from negative 0 .368 to infinity.
00:51
Increasing and decreasing, well, it looks like it's decreasing from negative infinity to our extrema.
01:05
And our x value there is negative 1.
01:07
So what i have to do is write negative 1.
01:10
Then it increases from negative 1 to infinity.
01:16
Let me slide this over.
01:18
See it just a little bit better when i have my graph.
01:20
Up.
01:21
There we go.
01:23
Boundedness.
01:25
Looks like it's bounded from above when y equals zero.
01:35
Extrema.
01:36
Here's an extrema right here because it's pointed out on decimal.
01:44
We can call this the minimum.
01:47
It's the lowest point on our graph.
01:50
Asymptotes, none, and behavior.
01:55
As the limit of this function, as x goes to negative infinity, or as we go to left, looks like it's just hovering by zero.
02:10
The limit of this function as x goes to positive infinity, well, it looks like it's going up forever or to positive infinity for our y values.
02:24
Pardon my squeaky chair.
02:26
All right, let's look at the next function, which is e to the negative x.
02:33
You get the screen so you can see it better...