Question

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.

Answer 1

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 ?

Answer 2

it is f(x)=x^3+8/x^2+x-6

Answer 3

assuming you really do mean

(x^3 + 8)/(x^2 + x - 6)
= (x+2)(x^2 - 2x + 4) / (x+3)(x-2)

It crosses the x-axis 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