Posted by logan on .
Given the function f(x)= x^3+8/x^2+6, determine the eqaution of the asymptotes and state the end behaviours of the graph near the asymptotes.

grade 12 math 
Reiny,
check you typing.
did you mean
f(x) = (x^3 + 8)/(x^2  6)
or is it the way you typed it?
What is with the +6 ? 
grade 12 math 
logan,
it is f(x)=x^3+8/x^2+x6

grade 12 math 
Anonymous,
assuming you really do mean
(x^3 + 8)/(x^2 + x  6)
= (x+2)(x^2  2x + 4) / (x+3)(x2)
It crosses the xaxis at x = 2
there are vertical asymptotes where the denominator is zero:
x = 3 or x=2
as x gets large, y > x^3/x^2 = x