Answer
r(x) has horizontal asymptote y=1.
Work Step by Step
All rational functions are in the form y = $\frac{ax^n + ...}{bx^m + ...}$, where n and m are the degrees of the numerator and denominator respectively.
To find the horizontal asymptote of r(x), we need to compare the degrees of the numerator and denominator.
r(x) = $\frac{(x+1)(x-2)}{(x+2)(x-3)}$ = $\frac{x^2-x-2}{x^2-x-6}$
Since the degrees (highest power) of the numerator and denominator are equal, the horizontal asymptote is $\frac{a}{b}$, or y = $\frac{1}{1}$ = 1.
