00:01
I'm going to be identifying the asymptopes.
00:03
So before i do that, i want to make sure that i factor and cancel any common factors.
00:09
So my numerator is the difference of cubes.
00:16
So it's going to look like that.
00:18
And on the bottom, it's just quadratic.
00:21
So i'm going to have x minus 3 times x minus 1.
00:28
Pardon me.
00:29
X minus 3 times x minus 1 right so i can see those x minus 3s whoops i didn't mean to do that those x minus 3s are going to cancel and that's good that we factored because that is not an asymptope that means we're going to have a hole there and we don't want to mistake that hole for an asymptote okay so here we go the vertical asymptope is just going to be at positive 1 so that's going to be x equals one.
01:07
Horizontal asymptopes.
01:09
No horizontal asymptote.
01:13
And that is because the degree on top is greater than the degree on the bottom.
01:18
You only have a horizontal if your degree is smaller on top or if the degrees are equal.
01:25
Since ours is bigger, we have no horizontal asymptope.
01:29
What we have instead is an oblique asymptope.
01:33
So we're going to do some long division to get the equation of that oblique asymptope.
01:41
X cubed, 0x squared, 0x minus 27.
01:47
Okay, x squared into x cubed, x times...