# How do you identify all asymptotes or holes and intercepts for f(x)=(1-x^3)/x?

Nov 10, 2016

A vertical asymptote is $x = 0$
The intercept with the x-axis is $\left(1 , 0\right)$

#### Explanation:

As you cannot divide by $0$, a vertial asymptote is $x = 0$

${\lim}_{x \to \pm \infty} f \left(x\right) = {\lim}_{x \to \pm \infty} \left(- {x}^{2}\right) = - \infty$

Intercepts, when $y = 0$ $\implies$ $x = 1$
Therefore the intercept is $\left(1 , 0\right)$

graph{(1-x^3)/x [-14.24, 14.24, -7.11, 7.12]}