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TV
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But for now, well, I want to show you how to find the vertical and the horizontal asymptote
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So what we're going to do to find the vertical and horizontal asymptote?
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First thing to find the vertical asymptote
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So if I want to find the vertical asymptote, all I need to do is set the bottom of the horizontal asymptote
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So what I'm doing is I'll subtract the one and divide by two
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Therefore x equals the name of 1-half
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Now on these questions, they also tell you what is the domain
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Well, if you guys remember when we're doing with rational functions, we have to set the bottom equal to 0 to find the domain as well
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Because if you guys look at it, when I have negative 1-half, if I put negative 1-half in frex, that gets me a negative 1
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Negative 1 plus 1 gives me 0, we can't divide by 0, right?
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So therefore the domain of this function is going to be all-real numbers except for x cannot equal a negative 1-half
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So just notice how the vertical asymptote and our domain are very similar, right?
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Because what your vertical asymptote is telling you is what values are not a part of your domain
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So they're very similar to it
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Then if we want to find the horizontal, there's a couple of rules that we need to look at
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And I'm just going to write some very arbitrary values and let's see what I have, M, let's do M is equal to N, M is less than N, and M is greater than N
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And so I know a lot of you are saying right now what that does M and M?
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Well, when you have a polynomial, what you're going to look at is you're going to look at your leading term, all right?
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You're leading coefficient. And what we'll see is up there for our leading coefficients, if this is my x value with the highest degree, this is going to be my leading term for each polynomial
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Right? Because members x squared plus x plus 1, that's my leading, that's the leading degree, that's the degree of my polynomial
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Well here I have a negative 5x plus 1, if I was to rewrite, if I was to rearrange this, well x is going to be my highest degree, so what is that value of x?
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Or am I sorry, what is the degree of my x? It's 1, right?
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And so what we say is in your rules we call this M, M is called the bottom degree N, so you just look at the degrees of your two polynomials, the degree of the top polynomial we call M, and the degree of the bottom polynomial we call N
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So if these two are equal to each other, which they are in this case, what we do is we take the coefficient
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We take the coefficient of them, so this would be a negative 5 divided by 2, is going to be your horizontal asymptote
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So you can say that, so your horizontal asymptote is going to be negative 5 halves
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And if M was less than N, I can say that my horizontal asymptote would equal 0, and if it was greater than, I would not have a horizontal asymptote
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So those are kind of three rules that you guys can use for horizontal asymptotes, vertical asymptotes, pretty similar, or I'm sorry very easy, just you set the bottom equation equal 0
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And if you have to look at the degree, and then determine which rule you're going to apply, if they're equal, you take the coefficients of the two leading terms and divide them
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If the top is less than the bottom's degree, then it's 0, and if it's the other way around then there's no verticals on them
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Any questions? Yes, I thought we were supposed to divide the top by the bottom, if the M and M are equal, like half the first, the numerator, the polynomial, no longer there, be divided by the polynomial
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I think what you're talking about is slant asymptotes, which happens when you have your M is greater than N, so it's a slant asymptote, it's not giving you a horizontal, which we'll get into later in class
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Now just with vertical horizontal and domain, that's all you guys can do. Alright?