document.write( "Question 1076155: The graph below has a vertical asymptote at x=3, a horizontal
\n" ); document.write( "asymptote at y=0, and passes through the point (4,2). what
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Algebra.Com's Answer #690863 by Edwin McCravy(20054)\"\" \"About 
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\n" ); document.write( ">>The graph below:<<
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document.write( "So it could have a denominator that when set = 0, gives\r\n" );
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document.write( "x=3,\r\n" );
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document.write( "So its denominator could be x-3.  So the equation could\r\n" );
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document.write( "be like this:   \"y=%22%3F%22%2F%28x-3%29\"\r\n" );
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\n" ); document.write( ">>a horizontal asymptote at y=0,<<
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document.write( "That means its numerator would have to be of less degree than \r\n" );
document.write( "its denominator.  So if its denominator is x-3, which is of \r\n" );
document.write( "degree 1, then its numerator would have to be of degree 0, \r\n" );
document.write( "which would be a constant, say, k.  Then the equation could\r\n" );
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document.write( "be like this:   \"y=%22k%22%2F%28x-3%29\"\r\n" );
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\n" ); document.write( ">>and passes through the point (4,2).
\n" ); document.write( "what could be the function of this graph?<<
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document.write( "We substitute x=4 and y=2 into\r\n" );
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document.write( "\"y=%22k%22%2F%28x-3%29\"\r\n" );
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document.write( "\"2=%22k%22%2F%284-3%29\"\r\n" );
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document.write( "\"2=%22k%22%2F1\"\r\n" );
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document.write( "\"2=k\"\r\n" );
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document.write( "So substituting k=2, the equation could be this function:\r\n" );
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document.write( "\"y=+2%2F%28x-3%29\"\r\n" );
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document.write( "or if we use function notation:\r\n" );
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document.write( "\"%22f%28x%29%22=+2%2F%28x-3%29\"\r\n" );
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document.write( "Edwin
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