00:02
Okay, on number nine, we are given a function of three, so this is f of x, equals three times x minus one squared times x plus five over two x to the fourth minus 12x cubed plus 16x squared.
00:31
So if you look at the top, it's not multiplied out, but if i were to multiply out, x squared times x that would be a 3x cubed as the largest variable on top plus all your other stuff on the bottom my largest would be 2x to the 4th so anytime that your numerator is smaller than your denominator exponent that means your horizontal asymptote is going to be at y equals 0 so as long as your numerator is smaller than your denominator it's going to be at y equals 0 for b you have g of x equals 2x squared minus 14x plus 20 over 2x squared plus 2x squared plus 2x minus 12 and again we're only concerned with your largest variable on top and bottom and since my exponents match when they're the same all you're going to look at is their leading coefficients, and you're going to make a ratio out of it.
01:54
So 2 divided by 2 is 1, so your horizontal asymptote is going to be at y equals 1.
02:04
On c, my h of x equals 1x minus 1 over 5x.
02:17
And again, i'm only concerned with my 1x and my 5x, and i'm only concerned with the 1 and the 5x.
02:24
Since these both have an exponent of one, i'm just going to take a ratio of their coefficients.
02:35
So my horizontal asymptote is going to be at y equals one -fifth.
02:44
Number 10.
02:47
So let's switch down to number 10.
02:49
This time they give you the information and they want you to write an equation for it.
02:54
So they give you your vertical asymptotes.
03:00
Are at x equals negative 4 and x equals negative 5 and they said that there was a multiplicity of 2.
03:10
So if there's a multiplicity of 2, that means that there's two of them.
03:15
So when we go to do our equation, i'll show you how that works.
03:20
Then they said we have x intercepts at 4 .0 and negative 6 .0.
03:28
And this one also has a multiplicity of 2.
03:31
And i'll show you how to represent that.
03:36
And then lastly, we have horizontal asymptotes at y equals 7...