Question

What are the asymptotes of `(x^3 + 2x + 2)/ (3x -1)`?

Answer 1

`x=1/3` graph{(x^3 + 2x + 2)/ (3x -1) [-10, 10, -5, 5]}

Explanation:

There are asymptotes when the denominator becomes zero.

Then, `3x-1=0`, so `x=1/3`.

Let's check `x=\oo`.

Since `oo^3` increases fast than `3*oo`, as `x` approaches infinity, `y` also approaches infinity. A similar argument can be constructed for `x=-oo`.