graph the ratinal function by hand

Question

graph the ratinal function by hand f(x)=(x^2-x-6/x^2-4)

Answer 1

(x^2-x+6)/(x^2-4) = (x-3)(x+2)/(x-2)(x+2) = (x-3)/(x-2)

f(x) has 2 x intercepts, (3,0), (-2,0)

vertical asymptotes: x=2, x=-2

horizontal asymptote = y=1