Question 937993
Like THIS:

f(x)=(x^2+2x-3)/(x^2+x-6)


Rendered into this:

{{{f(x)=(x^2+2x-3)/(x^2+x-6)}}}


Factor the parts.


{{{((x-1)(x+3))/((x-2)(x+3))}}}


One root, one vertical asymptote, one undefined point.


Root at x=1;
Vertical asymptote at x=2;
Discontinuous for x=-3.
Vertical Axis intercept  {{{x=1/2}}}.


{{{graph(300,300,-10,10,-10,10,(x^2+2x-3)/(x^2+x-6))}}}


Look again at the original function.  The degree of numerator and denominator are equal.  As x goes unbounded either to positive or to negative infinity, the two squared terms become increasingly more important to the value of f.  The value of the function approaches but never reaches 1.  <b>MEANING:  The horizontal asymptote is y=1.</b>