Date: 04/13/97 at 17:23:14 From: Nikita Bacchus Subject: Rational function Hi Dr. Math, Given the rational function y=r(x)=(4x^6-x^4)/(x^5+5) describe its end behavior and find all vertical and horizontal asymptotes for r if they exist. Would you need to factor?
Date: 04/14/97 at 10:20:03 From: Doctor Anthony Subject: Re: Rational function y = (4x^6 - x^4)/(x^5+5) = x^4(4x^2-1)/(x^5+5). There is a vertical asymptote where x^5 = -5 so x = -1.3797. The curve will go off to y = +infinity when just to the right of this asymptote and to y = -infinity when just to the left of this asymptote. The curve crosses the x-axis at x = -1/2 and at x = +1/2 and has multiple tangentcy at x = 0. When x increases to + or - infinity the curve becomes asymptotic to the line y = 4x -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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