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### Rational Function

```
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/
```
Associated Topics:
High School Calculus

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