SOLUTION: find the vertical, horizontal, and slant asymptotes, if any, for f(x)=5x^3+49x^2+127x+75/x^2+9x+18

Question 790305: find the vertical, horizontal, and slant asymptotes, if any, for f(x)=5x^3+49x^2+127x+75/x^2+9x+18
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You meant
f(x)=(5x^3+49x^2+127x+75)/(x^2+9x+18)=

Factoring, we get ,
and is divisible by
, so

So, and are vertical asymptotes,
and for ,

If we divide by ,
the quotient is and the remainder is .
In other words
So for and for ,
approaches as increases.
So is the slant asymptote on both sides.

IMPORTANT NOTE:
Those parentheses are essential if you cannot type the equation as the "two-story" version,
, with a long horizontal line in the middle.
The horizontal line implies the parentheses.
Without the parentheses, you get
f(x)=5x^3+49x^2+127x+75/x^2+9x+18=
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