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- anonymous

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

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- anonymous

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

- schrodinger

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- 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

\[\huge\rm y=\frac{ x^\color{ReD}{2}-4 }{ x^{\color{blue}{1}}+1 }\]
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

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

so factoring x^2 - 4 would be x- 2?

- Nnesha

no that wouldn't work sorry
we should divide

- anonymous

oh okay thats fine

- Nnesha

synthetic division or long which one is easy for u?

- anonymous

synthetic division does the one become -1 or stay the same

- 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

carry down the leading coefficient and then multiply bye -1 |dw:1444312872330:dw|
combine them 0 -1 = -1 and then repeat steps

- anonymous

ah I see one more thing real quick a negative * a negative is a positive right?

- Nnesha

yes negative times negative = positive :=)

- anonymous

so the final answer should be 1x^2-x-3?

- Nnesha

hmm when we divide by synthetic division
the degree of the answer should be one less than the original equation

- Nnesha

|dw:1444313248979:dw|

- Nnesha

does it make sense ? hmm

- anonymous

okay so its x-3 yeah!

- Nnesha

|dw:1444313357036:dw|

- anonymous

ohh Okay so its x-1 with a remainder of -3

- Nnesha

|dw:1444313566542:dw|

- Nnesha

yes right it's y =x-1 that's our oblique asy.

- anonymous

AHH Mrs Nnesha you are awesome and if I had a medal to give you I would Thank You so much

- Nnesha

np :=) hope that helpd

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