Question

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

Answer 1

A vertical asymptote is `x=0`
The intercept with the x-axis is `(1,0)`

Explanation:

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

`lim_(x->+-oo)f(x)=lim_(x->+-oo)(-x^2)=-oo`

Intercepts, when `y=0` `=>` `x=1`
Therefore the intercept is `(1,0)`

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