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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
