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

1 Answer
Nov 10, 2016

Answer:

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]}