anonymous
  • anonymous
How do you identify the oblique asymptote for a function y=x^2-4/x+1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Nnesha
  • Nnesha
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.
Nnesha
  • Nnesha
\[\huge\rm y=\frac{ x^\color{ReD}{2}-4 }{ x^{\color{blue}{1}}+1 }\] 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
anonymous
  • anonymous
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

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anonymous
  • anonymous
so factoring x^2 - 4 would be x- 2?
Nnesha
  • Nnesha
no that wouldn't work sorry we should divide
anonymous
  • anonymous
oh okay thats fine
Nnesha
  • Nnesha
synthetic division or long which one is easy for u?
anonymous
  • anonymous
synthetic division does the one become -1 or stay the same
Nnesha
  • Nnesha
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
Nnesha
  • Nnesha
carry down the leading coefficient and then multiply bye -1 |dw:1444312872330:dw| combine them 0 -1 = -1 and then repeat steps
anonymous
  • anonymous
ah I see one more thing real quick a negative * a negative is a positive right?
Nnesha
  • Nnesha
yes negative times negative = positive :=)
anonymous
  • anonymous
so the final answer should be 1x^2-x-3?
Nnesha
  • Nnesha
hmm when we divide by synthetic division the degree of the answer should be one less than the original equation
Nnesha
  • Nnesha
|dw:1444313248979:dw|
Nnesha
  • Nnesha
does it make sense ? hmm
anonymous
  • anonymous
okay so its x-3 yeah!
Nnesha
  • Nnesha
|dw:1444313357036:dw|
anonymous
  • anonymous
ohh Okay so its x-1 with a remainder of -3
Nnesha
  • Nnesha
|dw:1444313566542:dw|
Nnesha
  • Nnesha
yes right it's y =x-1 that's our oblique asy.
anonymous
  • anonymous
AHH Mrs Nnesha you are awesome and if I had a medal to give you I would Thank You so much
Nnesha
  • Nnesha
np :=) hope that helpd

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