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