Question 890057
r(x) = x^2+x-72/ x^2-x-56

The correct text form you want is  r(x)=(x^2+x-72)/(x^2-x-56)

and as rendered looks like {{{r(x)=(x^2+x-72)/(x^2-x-56)}}}




Factor if you can.
{{{r(x)=((x-8)(x+9))/((x+7)(x-8))}}}.
A discontinuity occurs at x=8.  This is because of the factor {{{(x-8)/(x-8)}}}.
A vertical asymptote will occur at x=-7 because the function is undefined there.


Domain:  {{{-infinity<x<-7}}} U  {{{-7<x<8}}} U  {{{8<x<infinity}}}.


{{{graph(300,300,-15,10,-15,10,(x^2+x-72)/(x^2-x-56))}}}

The graph will not display properly the discontinuity at x=8 but it is there.  The HORIZONTAL asymptote is y=1.   This might be easier to understand if you take your original function before factoring and examine what happens for x extremely large or small without bound.  The x^2 terms in numerator and denominator become increasingly far more important, so each approaches the same square value, and you have the ratio of these.