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Asymptotes

Rules
by

Michelle Barnhill

on 27 July 2010

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Transcript of Asymptotes

Asymptotes Vertical Asymptotes Find any vertical asymptote by:
1) Set denominator = 0



2) Solve for x



3) So, x = 3 is a Vertical Asymptote 2x +4
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x - 3 x -3 = 0 x = 3 Other Asymptotes a) If the numerator has a LOWER DEGREE
than the denominator, there is a
horizontal asymptote, y = 0 (the x-axis) b) If the numerator and the denominator
have the SAME DEGREE, and the function is in the form of a fraction, the horizontal asymptote is the fraction created by the coefficient of the term with the highest degree in the numerator over the coefficient of the term with the highest degree in the denominator. 4x + 3 5x -6 The horizontal asymptote is y = 4/5 The vertical asymptote is x = 6/5 -5 x^2 - 3x -10 The horizontal asymptote is y = 0 The vertical asymptotes are
x = 5 and x = -2

***x^2 - 3x - 10 becomes
(x - 5)(x + 2)
x - 5 = 0 and x + 2 = 0
x = 5 x = -2
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