Question 889563
f(x)=(5x)/(x^2-x-6)


Should render with the triple brace tags as {{{f(x)=(5x)/(x^2-x-6)}}}


There is an x-axis intercept at x=0.

{{{f(x)=(5x)/((x+2)(x-3))}}}
Vertical asymptotes are at x=-2 and x=3, at which f is undefined.
Domain is {{{-infinity<x<-2}}} and {{{-2<x<3}}} and {{{3<x<infinity}}}.

f approaches 0 as x tends to negative or positive infinity, so the horizontal asymptote is {{{y=0}}}.


{{{graph(300,300,-6,6,-6,6,(5x)/(x^2-x-6))}}}


to show horizontal asymptote location better,
{{{graph(300,300,-20,20,-20,20,(5x)/(x^2-x-6))}}}