Lines that a function approaches but does NOT actually touch.

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Presentation transcript:

Lines that a function approaches but does NOT actually touch

 Factor the Denominator (and numerator)  Do the Numerator and Denominator have common Factors? If so, cancel.  Set the Denominator equal to zero.  Solve for x. A. f(x)= x B. f(x)= x+3 C. X x 2 -9 x 2 -9 x 2 +9

 f(x) = x 2 – 4x x 2 -7x+12

 Compare the Degree of the Numerator and Denominator.  If largest on top, then NO Horizontal Asymptote.  If largest on bottom, then HA is y=0  If equal, the ratio of the leading coefficients is the HA f(x)= 8x+3f(x)= 8x 2 +3f(x)=8x x 2 +14x 2 +14x 2 +1

 Find the HA (if one exists) of the rational functions f(x)= 7x 3 +x-2 -4x 3 +1 f(x)= x 2 +3x+2 x-2

 Find all vertical and horizontal asymptotes (if there are any).  f(x)=X 2 +2x-8 3x 2 -5x-2