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document.write( "Find the verticle asymptote of the rational \r\n" );
document.write( "function 
\r\n" );
document.write( "Possible answers: \r\n" );
document.write( "y = 1/2\r\n" );
document.write( "y = 3/4\r\n" );
document.write( "y = 2\r\n" );
document.write( "y = 4 \r\n" );
document.write( "Thank you. Exactly what is a asymptote? Can anyone \r\n" );
document.write( "explain the simplest way to solve this problem?\r\n" );
document.write( "\r\n" );
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document.write( "\r\n" );
document.write( "Something is wrong! Asymptotes are straight \r\n" );
document.write( "lines. All those choices are equations of \r\n" );
document.write( "HORIZONTAL lines, not of VERTICAL lines. \r\n" );
document.write( "Yet you asked for the VERTICAL asymptote. The \r\n" );
document.write( "vertical asymptote has equation 
and the \r\n" );
document.write( "HORIZONTAL asymptote has equation 
. \r\n" );
document.write( "Did you copy something wrong? Did you type y's \r\n" );
document.write( "where there should be x's, or did you type \"verticle\" \r\n" );
document.write( "(sic) when you meant \"horizontal\"?\r\n" );
document.write( "\r\n" );
document.write( "First I'll have to show you how to solve the \r\n" );
document.write( "problem by graphing. Then I'll show you the simplest \r\n" );
document.write( "way. But you must understand what an asymptote\r\n" );
document.write( "is before you can know what you are doing.\r\n" );
document.write( "\r\n" );
document.write( "Let's graph \r\n" );
document.write( "Get some points:\r\n" );
document.write( "\r\n" );
document.write( " x f(x)\r\n" );
document.write( "-10 1\r\n" );
document.write( "-7 1.1\r\n" );
document.write( "-3 1.5\r\n" );
document.write( "-2 1.8\r\n" );
document.write( "0 6\r\n" );
document.write( "2 -1\r\n" );
document.write( "4 0\r\n" );
document.write( "8 .4\r\n" );
document.write( "11 .5 \r\n" );
document.write( "\r\n" );
document.write( "
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document.write( "\r\n" );
document.write( "The graph of the function is in green. But \r\n" );
document.write( "I have drawn two extra lines in, a blue vertical \r\n" );
document.write( "line and a red horizontal line. These lines are\r\n" );
document.write( "called \"asymptotes\". Look at the blue vertical \r\n" );
document.write( "line that goes through 1/2 on the x-axis? The \r\n" );
document.write( "green curve approaches that green line but never \r\n" );
document.write( "touches it. That line is called the vertical \r\n" );
document.write( "ASYMPTOTE. I also drew in the horizontal \r\n" );
document.write( "asymptote in red.\r\n" );
document.write( "\r\n" );
document.write( "As you can see, that green vertical asymptote has \r\n" );
document.write( "the equation 
. and that blue \r\n" );
document.write( "horizontal asymptote has the equation 
.\r\n" );
document.write( "\r\n" );
document.write( "Now here is the easy way to find the equation of that blue \r\n" );
document.write( "vertical asymptote without having to graph:\r\n" );
document.write( "\r\n" );
document.write( "Set the denominator of equal\r\n" );
document.write( "to zero, because a function is undefined if x has a value\r\n" );
document.write( "which causes the function to be undefined. You know\r\n" );
document.write( "that having a 0 in the denominator causes a fraction to be\r\n" );
document.write( "undefined, right? So we have\r\n" );
document.write( "\r\n" );
document.write( "
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document.write( " 
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document.write( " \r\n" );
document.write( "\r\n" );
document.write( "That's all there is to finding the equation of the vertical \r\n" );
document.write( "asymptote.\r\n" );
document.write( "\r\n" );
document.write( "Now to find the horizontal asymptote, the red line. \r\n" );
document.write( "Since numerator and denominator have the same degree \r\n" );
document.write( "(same largest exponent of x), we merely get the \r\n" );
document.write( "quotient of the coefficients of the largest powers \r\n" );
document.write( "of x. The coefficient of x in the numerator is 3 \r\n" );
document.write( "and the coefficient of x in the denominator is\r\n" );
document.write( "4, so we make the fraction
and write\r\n" );
document.write( " as the equation of the red horizontal \r\n" );
document.write( "asymptote.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
