Given the following rational function, find

Question

a) the horizontal asymptote(s),
b) the vertical asymptote(s), if any, and
c) the oblique asymptote(s), if any.

F(x) = x^2-x-2/2x^2-x-2

Answer 1

a long division shows that

F(x) = 1/2 - (x+2)/(2(2x^2-x-2))

so, as x gets large, F(x) -> 1/2

vertical asymptotes where 2x^2-x-2=0

no oblique asymptotes.