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all right what I'd like to do is show

you guys how to find the slant

asymptotes all right I'm sorry let's

find the vertical and let's find a

horizontal vertical horizontal slip okay

so the first thing I like to start with

vertical and when finding the vertical

asymptotes

all right what would you do is we need

to find out what values are not going to

be true for x-ray because vertical is

you're going to think of like my graph

here vertical are gonna be part of the

lines so we're gonna have X values that

my graph are going to approach but

they're never gonna touch or ever gonna

cross so therefore it and we have to

find a certain X values that are not a

part of our function so when you dealing

with a rational function we know that if

we find values that make the bottom of

zero those cannot be a part of our

function because you cannot divide by

zero so to find those values that makes

our bottom time knowing of zero I need

to set our bottom polynomial equal to

zero then when I solve I get one equals

x squared when I take the square root I

get x equals plus or minus one

therefore I have two per classes so you

know let's do a little sketch graph here

so you can see so if I have

we're not negative one and that one all

right those are two that my

crap is never going to touch it's just

gonna keep our approachment keep on

approaching it without plowing we like

to say when you're checking out my

horizontal there's three rolls I'll try

to say that as slowly as possible

because I made a couple videos on this

and I don't want to write them down

again so if you want me to see what

they're written down check out some of

my other videos on asking jokes but for

horizontal we need to look at the

degrees of your leading term when I look

at the degrees of the leading term if

your if your degree of your top term or

top polynomial is less than your degree

of your bottom paano mil then your

horizontal is a scope is when y equals 0

if these two degrees were equal to each

other then you need to take the

coefficient of each of those leading

terms and divide them and that put Y

would equal as your horizontal asymptote

in this case though when you have your

degree on your upon moment is larger

than a degree on the bottom polynomial

you do not have a horizontal asymptote

what you have is what we call a slant

asymptote

and a fine slant asymptotes what we're

going to do is we're gonna have to use

long division and the reason why I want

to use long division is because one

thing pours that our own new synthetic

division remember it always had to be in

the form of a factor right and you have

to use that zero to do this well here we

don't have a factor you know we're not

looking for factors or zeros so simple

long division is going to give us our

quickest method and area to find our

horizontal asymptote so less you long to

finish it remember you take your first

term divide it in two I'm sorry actually

that's right there when doing the long

division of this sort we need to make

sure every term is created so I don't

have a zero X I need to create one okay

notice that my divisor is x squared

minus one well to finish up this problem

I got to make sure that every single X

term is is is represented when dividing

so if x squared goes into x cubed x

times x squared times X cubed or x

squared is X cubed all right x times

zero X is still going to give you my

zero x squared and next time

was gonna give me a negative 1x

obviously I have nothing left over here

to bring down

so therefore what you do is so I'll have

0 right so 0 minus so that was cancel

out that's 0 0 minus a negative 1 give

me a positive x so x over x squared

minus 1 so we're not concerned about the

remainder though all right we don't care

about the manor all our concern about is

what our divisor is without the

remainder so therefore my horizontal

asymptote is going to be this X line

which looks like that

so therefore this is another line that

my graph is going to approach and but

it's not going to cross it or it's not

going to not get across it

normal touch it so without you know

without doing a table of values or

without looking graphically we won't

know what the graph looks like but you

can at least see where the graph is not

going to touch and it will approach that

to me that's how you find your

horizontal slant and vertical asymptote