college algebra
posted by ladybug .
Given the following rational function, find:
A. horizontal asymptotes
B. vertical asymptote(s), if any
C. oblique asymptote(s), if any
f(x)=x^2x2/2x^2x21

y = (x2)(x+1)/((x+3)(2x7) )
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