SOLUTION: How many asymptotes does R(x)=x^3-1/x^2-1 have? a. 3 b. 0 c. 2 d. 1

Question 141009: How many asymptotes does R(x)=x^3-1/x^2-1 have?
a. 3
b. 0
c. 2
d. 1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many asymptotes does R(x)=x^3-1/x^2-1 have?
a. 3
b. 0
c. 2
d. 1
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Factor to get:
R(x) = [(x-1)(x^2+3x^2+3x+1]/[(x+1)(x-1)]
--------------
Oblique asymptote:
Since the degree of the denominator is less than the degree of
the numerator, divide to get R(x) = x +[(x-1)/(x^2-1)]
Then y=x is an oblique asymptote.
---------
Horizontal asymptote:
Since the degree of the numerator is greater than the degree
of the denominaot, there is no horizontal asymptote.
--------------
Since there is a factor of (x-1) in numerator and denominator,
there is a hole at x=1
----------------
Vertical Asymptote:
Since (x+1) is a factor of the denominator, x=-1 is a vertical symptote.
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Cheers,
Stan H.

Cheers,
Stan H.

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