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Find the horizontal for oblique asymptote of f(x)=-3x^2+7x+1/x-2

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For greater clarity, please enclose the divisor (x-2) inside parentheses. Thx.

Divide x-2 into 3x^2 + 7x + 1:

3x + 13
__________________
x-2 / 3x^2 + 7x + 1
3x^2 - 6x
----------------
13x + 1
13x - 26
----------------
-27 (remainder)
-27
The quotient here is 3x + 13 - ------
x-2

The slant asymptote is the line y = 3x + 13. Note that -27 / (x-2) goes to zero as x grows large in either direction (positive or neg).

Note that you are looking for the "oblique" or "slant" asymptote here; there is no "horizontal" involved.


User Sean Heiss
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