document.write( "Question 205136: Please help me graph and label all asymptotes of y=2x/x-4\r
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Algebra.Com's Answer #154863 by Edwin McCravy(20060) $\"\"$ $\"About$

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Please help me graph and label all asymptotes of $\"y=%282x%29%2F%28x-4%29\"$
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document.write( "To find the vertical asymptote, set the denominator equal\r\n" );
document.write( "to zero and solve for x:\r\n" );
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document.write( " is the equation of a vertical line 4 units right of\r\n" );
document.write( "the y-axis, so we draw that vertical asymptote:\r\n" );
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document.write( "There will be a horizontal asymptote whenever the (degree) largest\r\n" );
document.write( "exponent of x in the top is not larger than the largest\r\n" );
document.write( "exponent of x in the bottom.  When the degrees of the top is\r\n" );
document.write( "smaller, the horizontal asymptote is the line  but\r\n" );
document.write( "when the degrees are the same the horizontal asymptote is\r\n" );
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document.write( "The coefficient of x on the top is 2, and the coefficient of x\r\n" );
document.write( "on the bottom is 1, so the horizontal asymptote is  or\r\n" );
document.write( ". That is a horizontal line 2 units above the x-axis.\r\n" );
document.write( "Let's draw it:\r\n" );
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document.write( "Now we need to get some points on both sides of all asymptotes:\r\n" );
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document.write( "(-4,1), (0,0), (2,-2), (3,-6), (5,10), (6,6), (8,4)\r\n" );
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document.write( "Plot those points:\r\n" );
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document.write( "Draw a smooth graph through the points:\r\n" );
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document.write( "The vertical asymptote is \r\n" );
document.write( "The horizontal asymptote is \r\n" );
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document.write( "Edwin

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