anonymous
  • anonymous
State the horizontal asymptote of the rational function.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
numerator degree is 1, denominator has degree 2 and since 2 is larger than 1 the horizontal asymptote is \(y=0\)
anonymous
  • anonymous
for the vertical asymptotes, set the denominator equal to zero and solve for \(x\)
anonymous
  • anonymous
i dont get how you got y=o pplz help with horizontal

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anonymous
  • anonymous
if the degree of the numerator is smaller than the degree of the denominator, you will have a horizontal asymptote at \(y=0\) aka the \(x\)- axis do you know what i mean by degree?
anonymous
  • anonymous
yeah i know what degree is
anonymous
  • anonymous
what if the degree of the numnater is bigger
anonymous
  • anonymous
ok then that is all you need to consider think about what would happen if you put in say \(x=10^6\) you would have a million in the numerator but you would have \(10^{12}\) in the denominator, and get a very small number (close to zero)
anonymous
  • anonymous
if the degree of the numerator is larger, no horizontal asymptote
anonymous
  • anonymous
and if the degrees are the same, it is the ratio of the leading coefficients
anonymous
  • anonymous
so its allways y=0 when the top is smaller and none when the top is larger
anonymous
  • anonymous
yes, always
anonymous
  • anonymous
and if they are the same, for example \[\frac{2x^2+3x-3}{5x^2+10}\] i would be \(y=\frac{2}{5}\)
anonymous
  • anonymous
why 5?
anonymous
  • anonymous
you got that? three cases 1) top is larger: none 2) bottom is larger :\(y=0\) 3) the degrees are equal: \(y=\text{ratio of leading coefficients}\)
anonymous
  • anonymous
in my example \[\frac{2x^2+3x-3}{5x^2+10}\] the degrees are both two the leading coefficient of the numerator is 2 the leading coefficent of the denominator is 5 so horizontal asymptote is \(y=\frac{2}{5}\)
anonymous
  • anonymous
State the horizontal asymptote of the rational function. 9x^2-3x-8 --------- 4x^2-5x+3 so this would be y=9/4?
anonymous
  • anonymous
sure would
anonymous
  • anonymous
thanks your the best!! can you fan me so i can message you if i need help plz?
anonymous
  • anonymous
you have to admit this is rather easy, right? i mean once you know what you are doing
anonymous
  • anonymous
k
anonymous
  • anonymous
yeah i posted this because i am home schooled and i have no one to teach me the concepts
anonymous
  • anonymous
that must be tough guess you can always post here. there are lots of on line resources, but here you may get a direct answer

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