Posted by **ladybug** on Saturday, November 10, 2012 at 6:04pm.

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

- college algebra -
**Reiny**, Saturday, November 10, 2012 at 6:32pm
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

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