3'6 Asymptotes

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3.6 Asymptotes
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Vertical Asymptotes

• The line xc is a vertical asymptote of the
  function f if

With rational functions, the vertical asymptotes
will be precisely when the denominator is zero.
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Horizontal Asymptotes

• The line yL is a horizontal asymptote of the
  function f if

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Rational functions Horizontal Asymptotes

• Let f(x)p(x)/q(x) be a rational function.
• Let mdegree of p(x), n degree of q(x).
• Divide p(x) and q(x) by xn
• Find the limit using lim 1/xr0 for rgt0.

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Rational functions Horizontal Asymptotes

• Let f(x)p(x)/q(x) be a rational function.
• Let mdegree of p(x), n degree of q(x).
• If mltn, y0 is the horizontal asymptote
• If mn, ya/b where a and b are the leading
  coefficients of p(x) and q(x) respectively
• If mgtn, there is no horizontal asymptote.

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