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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