# How do you find the vertical, horizontal and slant asymptotes of: f(x)= x^(1/3)?

Jun 26, 2018

No vertical asymptotes as all values of $x$ are valid in $f \left(x\right)$

No slant asymptotes as not a quotient.

No horizontal asymptote.

#### Explanation:

Our function $f$ is continuous and therefore has no vertical asymptotes.

No slant asymptotes as not a quotient.

Horizontal asymptote when ${\lim}_{x \to - \infty} = k {\lim}_{x \to \infty} = k$ where$k \cancel{=} - \infty , \infty$

${\lim}_{x \to 00} {x}^{\frac{1}{3}} = \infty$

No horizontal asymptote.