document.write( "Question 39839: Need help with the following:\r
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Algebra.Com's Answer #25277 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
Need help with the following:\r\n" );
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document.write( "Find a rational function that has x=2 and  x=-1 as vertical\r\n" );
document.write( "asymptotes, and  (4,0)  as an x-intercept.\r\n" );
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document.write( "A rational function is a fraction, so we write y = a fraction bar:\r\n" );
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document.write( "                \r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧\r\n" );
document.write( "     \r\n" );
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document.write( "To have a vertical asymptote of x = 2 we must have gotten that equation by\r\n" );
document.write( "setting one of the factors of the denominator = 0 and solving for x.\r\n" );
document.write( "To have gotten x = 2, we must have set x - 2 = 0.  Therefore (x - 2)\r\n" );
document.write( "must be a factor of the denominator. So we now have\r\n" );
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document.write( "          \r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧\r\n" );
document.write( "     (x - 2)\r\n" );
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document.write( "To have a vertical asymptote of x = -1 we must have gotten that equation by\r\n" );
document.write( "setting one of the factors of the denominator = 0 and solving for x.\r\n" );
document.write( "To have gotten x = -1, we must have set x + 1 = 0.  Therefore (x + 1)\r\n" );
document.write( "must be a factor of the denominator.  So we now have\r\n" );
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document.write( "          \r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧\r\n" );
document.write( "     (x - 2)(x + 1)\r\n" );
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document.write( "To have (4,0) as an x-intercept, y must be 0 when x = 4.  So the numerator\r\n" );
document.write( "could have as a factor x - 4, since that is 0 when x = 4.  So the easiest\r\n" );
document.write( "answer is\r\n" );
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document.write( "         x - 4 \r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧\r\n" );
document.write( "     (x - 2)(x + 1)\r\n" );
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document.write( "or you can multiply the bottom out if you like and get\r\n" );
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document.write( "       x - 4 \r\n" );
document.write( "y = 覧覧覧覧覧覧\r\n" );
document.write( "     xｲ - x - 2\r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
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