Aktuel tid:0:00Samlet varighed:3:16

0 energipoint

Studying for a test? Prepare with these 10 lessons on Rational relationships.

See 10 lessons

# Graphs of rational functions: horizontal asymptote

Video transskription

let FFXIII go negative x squared plus a
X plus be over X squared plus he explicitly were ABC and D are unknown
constants which of the following is a possible graph of Y is equal to
vaccinate else dashed lines indicate a sumptuous this is really interesting
year and they give us four choices we see 430 home right now that if I school
little bit over you can see choice D and so I encourage you to pause the video
and think about how you can figure it out because it is interesting that they
haven't given us a lot of details they haven't given us what these coefficients
are these constants are going to be all right now let's think about it so one
day we can think about is horizontal asymptotes so let's think about what
happens as X approaches positive or negative infinity well as X so as as X
approaches infinity or acts approaches negative infinity after effects after
effects is going to be approximately equal to look at the highest degree
terms because these are going to dominate as the magnitude of Acts the
absolute value of x becomes very large so after effects is going to be
approximately negative x squared over X squared which is equal to negative or we
could another way to think about it this is the same thing as negative one so a
fax is going to approach of AX is going to approach negative one in either
direction as X approaches infinity or X approaches negative it is we have a
horizontal asymptotes at Y equals negative won the seat twice a year it
does look like they have a horizontal asymptotes why is equal to negative one
right over there and we can verify that because each each hash mark is to go
from 202 negatives 22 negative force of this does look like it's a negative 10
just based only on the horizontal asked to trace a looks good choice be we have
a horizontal asymptotes at Y is equal to positive too so we can rule we can rule
that out out we know that our horizontal
asymptotes as X approaches positive or negative infinity is at negative what y
equals negative on here are horizontal asymptotes is a twat is equal to 0 the
graph approaches it approaches the x-axis from either above or below its
not the horizontal asymptotes is not y equals negative one so we can rule that
one out and then similarly over here or horizontal asymptotes is not like was
negative on Iran to last until it is why is equal to 0 so we can rule that went
out and that makes sense because really they only gave us enough information to
figure out the horizontal asymptotes they didn't give us enough information
to figure out how many routes or what happens in the interim role in all of
those type of things how many zeros and all of that but we don't know what the
what the actual with the actual coefficients are constants of the
quadratic are all we know is what happens as the X where terms dominate
this thing is going to approach negative one and so we picked choice choice a