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

Apr 25, 2017

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

#### Explanation:

There are asymptotes when the denominator becomes zero.

Then, $3 x - 1 = 0$, so $x = \frac{1}{3}$.

Let's check $x = \setminus \infty$.

Since ${\infty}^{3}$ increases fast than $3 \cdot \infty$, as $x$ approaches infinity, $y$ also approaches infinity. A similar argument can be constructed for $x = - \infty$.