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anonymous

  • one year ago

How do you identify the oblique asymptote for a function y=x^2-4/x+1

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  1. Nnesha
    • one year ago
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    not all functions have oblique asymptote if the degree of the numerator one larger than the denominaotr degree then you can find slant(oblique)asy.

  2. Nnesha
    • one year ago
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    \[\huge\rm y=\frac{ x^\color{ReD}{2}-4 }{ x^{\color{blue}{1}}+1 }\] highest degree of the numerator is 2 and the denominator is one so we can find oblique asy divide x^2-4 by x+1 using long division or synthetic division btw for this question you can factor x^2 -4

  3. anonymous
    • one year ago
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    so the degree of the numerator is bigger than that which is the denominator so this one will be a slant how do you find a slant

  4. anonymous
    • one year ago
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    so factoring x^2 - 4 would be x- 2?

  5. Nnesha
    • one year ago
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    no that wouldn't work sorry we should divide

  6. anonymous
    • one year ago
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    oh okay thats fine

  7. Nnesha
    • one year ago
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    synthetic division or long which one is easy for u?

  8. anonymous
    • one year ago
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    synthetic division does the one become -1 or stay the same

  9. Nnesha
    • one year ago
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    yes right we should solve for x x+1 = 0 x=-1 |dw:1444312769154:dw| x^2 -4 is same as x^2 +0x - 4 we should write highest degree to lowest so that's why i wrote 0 there

  10. Nnesha
    • one year ago
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    carry down the leading coefficient and then multiply bye -1 |dw:1444312872330:dw| combine them 0 -1 = -1 and then repeat steps

  11. anonymous
    • one year ago
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    ah I see one more thing real quick a negative * a negative is a positive right?

  12. Nnesha
    • one year ago
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    yes negative times negative = positive :=)

  13. anonymous
    • one year ago
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    so the final answer should be 1x^2-x-3?

  14. Nnesha
    • one year ago
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    hmm when we divide by synthetic division the degree of the answer should be one less than the original equation

  15. Nnesha
    • one year ago
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    |dw:1444313248979:dw|

  16. Nnesha
    • one year ago
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    does it make sense ? hmm

  17. anonymous
    • one year ago
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    okay so its x-3 yeah!

  18. Nnesha
    • one year ago
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    |dw:1444313357036:dw|

  19. anonymous
    • one year ago
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    ohh Okay so its x-1 with a remainder of -3

  20. Nnesha
    • one year ago
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    |dw:1444313566542:dw|

  21. Nnesha
    • one year ago
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    yes right it's y =x-1 that's our oblique asy.

  22. anonymous
    • one year ago
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    AHH Mrs Nnesha you are awesome and if I had a medal to give you I would Thank You so much

  23. Nnesha
    • one year ago
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    np :=) hope that helpd

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