Question

Given the following rational function, find:
A. horizontal asymptotes
B. vertical asymptote(s), if any
C. oblique asymptote(s), if any

f(x)=x^2-x-2/2x^2-x-21

Answer 1

y = (x-2)(x+1)/((x+3)(2x-7) )

a) as x --->∞
the curve is approximated by
y = x^2/2x^2 = 1/2
approaching from below y=1/2 for positive x's
and approaching from above y = 1/2 for negative large x's
Anyway, y = 1/2 is the horizontal asymtote

b) at vertical asymptotes, the denominator is zero, so
x = -3 and x = 7/2 are vertical asymptotes

c) since the numerator and denominator are of the same degree, there is no oblique asymptote