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sara1234

State the horizontal asymptote of the rational function.

  • one year ago
  • one year ago

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  1. satellite73
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    numerator degree is 1, denominator has degree 2 and since 2 is larger than 1 the horizontal asymptote is \(y=0\)

    • one year ago
  2. satellite73
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    for the vertical asymptotes, set the denominator equal to zero and solve for \(x\)

    • one year ago
  3. sara1234
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    i dont get how you got y=o pplz help with horizontal

    • one year ago
  4. satellite73
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    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?

    • one year ago
  5. sara1234
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    yeah i know what degree is

    • one year ago
  6. sara1234
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    what if the degree of the numnater is bigger

    • one year ago
  7. satellite73
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    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)

    • one year ago
  8. satellite73
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    if the degree of the numerator is larger, no horizontal asymptote

    • one year ago
  9. satellite73
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    and if the degrees are the same, it is the ratio of the leading coefficients

    • one year ago
  10. sara1234
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    so its allways y=0 when the top is smaller and none when the top is larger

    • one year ago
  11. satellite73
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    yes, always

    • one year ago
  12. satellite73
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    and if they are the same, for example \[\frac{2x^2+3x-3}{5x^2+10}\] i would be \(y=\frac{2}{5}\)

    • one year ago
  13. sara1234
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    why 5?

    • one year ago
  14. satellite73
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    you got that? three cases 1) top is larger: none 2) bottom is larger :\(y=0\) 3) the degrees are equal: \(y=\text{ratio of leading coefficients}\)

    • one year ago
  15. satellite73
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    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 \(y=\frac{2}{5}\)

    • one year ago
  16. sara1234
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    State the horizontal asymptote of the rational function. 9x^2-3x-8 --------- 4x^2-5x+3 so this would be y=9/4?

    • one year ago
  17. satellite73
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    sure would

    • one year ago
  18. sara1234
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    thanks your the best!! can you fan me so i can message you if i need help plz?

    • one year ago
  19. satellite73
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    you have to admit this is rather easy, right? i mean once you know what you are doing

    • one year ago
  20. satellite73
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    k

    • one year ago
  21. sara1234
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    yeah i posted this because i am home schooled and i have no one to teach me the concepts

    • one year ago
  22. satellite73
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    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

    • one year ago
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