document.write( "Question 1200447: Write an equation for a rational function with:\r
\n" ); document.write( "\n" ); document.write( "Vertical asymptotes at x = -6 and x = 5\r
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\n" ); document.write( "\n" ); document.write( "Horizontal asymptote at y = 7 \n" ); document.write( "
Algebra.Com's Answer #834577 by ikleyn(52873)\"\" \"About 
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\n" ); document.write( "Write an equation for a rational function with:\r
\n" ); document.write( "\n" ); document.write( "Vertical asymptotes at x = -6 and x = 5\r
\n" ); document.write( "\n" ); document.write( "x intercepts at x = -4 and x = -3\r
\n" ); document.write( "\n" ); document.write( "Horizontal asymptote at y = 7
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document.write( "This rational function wants to have binomial factors (x+6) and (x-5)\r\n" );
document.write( "in the denominator to provide the necessary asymptotes\r\n" );
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document.write( "and binomial factors (x+4) and (x+3) in the numerator to provide the necessary x-intercepts.\r\n" );
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document.write( "So, we write\r\n" );
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document.write( "    f(x) = \"a%2A%28%28%28x%2B4%29%2A%28x%2B3%29%29%2F%28%28x%2B6%29%2A%28x-5%29%29%29\"\r\n" );
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document.write( "with coefficient \"a\".\r\n" );
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document.write( "Horizontal asymptote y= 7 means that  { limit f(x) }  is 7 when x tends to +oo  or -oo,\r\n" );
document.write( "which means that a= 7.\r\n" );
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document.write( "Finally, the function is  f(x) = \"7%2A%28%28%28x%2B4%29%2A%28x%2B3%29%29%2F%28%28x%2B6%29%2A%28x-5%29%29%29\".    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Use free of charge online plotting tool at this web-site\r
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\n" ); document.write( "\n" ); document.write( "www.desmos.com/calculator \r
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\n" ); document.write( "\n" ); document.write( "to plot the graph of the function and to see visually that the function has all necessary properties.\r
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