How do you find the asymptotes for #f(x) = x / (3x(x-1))#?

1 Answer
Nov 11, 2016

Answer:

The vertical asymptote is #x=1#
The horizontal asymptote is #y=0#

Explanation:

You can simplify #f(x)=1/(3(x-1))#
As you cannot divide by #0#, the vertical asymptote is #x=1#

There are no slant asymptotes since the degree of the numerator #<# the degree of the denominator

#lim_(x->-oo)f(x)=lim_(x->-oo)1/(3x)=0^(-)#

#lim_(x->+oo)f(x)=lim_(x->+oo)1/(3x)=0^(+)#

So #y=0# is a horizontal asymptote.
graph{1/(3(x-1)) [-7.9, 7.9, -3.95, 3.95]}