college algebra

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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 -

    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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