document.write( "Question 78340: Can you tell me if this answer is correct?
\n" ); document.write( "Determine the vertical asympotes for the function \r
\n" ); document.write( "\n" ); document.write( "f(x)= $\"%28x%5E2-16%29%2F%283x%5E2-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "My answer:\r
\n" ); document.write( "\n" ); document.write( " $\"x=0\"$ , $\"x=sqrt%281%29\"$ , $\"x=+-sqrt%281%29\"$
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Algebra.Com's Answer #56188 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Can you tell me if this answer is correct?\r\n" );
document.write( "Determine the vertical asympotes for the function \r\n" );
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document.write( "My answer:\r\n" );
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document.write( ", , \r\n" );
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document.write( "The  is incorrect!  The other two are correct\r\n" );
document.write( "except that you would never leave those answers\r\n" );
document.write( "unsimplified as  and \r\n" );
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document.write( "Since , the answers should be \r\n" );
document.write( "simplified as:\r\n" );
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document.write( " and \r\n" );
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document.write( "You simply set the denominator of\r\n" );
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document.write( "equal to 0\r\n" );
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document.write( "Divide every term on both sides through by 3\r\n" );
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document.write( "There are two ways to solve that:\r\n" );
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document.write( "1. Factor the left side as the difference\r\n" );
document.write( "of squares:\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "Setting the first factor = 0,\r\n" );
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document.write( "Setting the second factor = 0,\r\n" );
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document.write( "2. The way you apparently did it:\r\n" );
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document.write( "Add + to both sides\r\n" );
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document.write( "Take square roots of both sides\r\n" );
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document.write( " and \r\n" );
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document.write( "which simplifies to\r\n" );
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document.write( " and \r\n" );
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document.write( "That is perfectly OK.\r\n" );
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document.write( "[But there is no way you could have \r\n" );
document.write( "gotten !]\r\n" );
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document.write( "Let's look at the graph of \r\n" );
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document.write( "Now let's draw in the two vertical \r\n" );
document.write( "asymptotes at x=-1 and a=1:\r\n" );
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document.write( "and you can see that the curve approches \r\n" );
document.write( "those two asymptotes on both sides. The\r\n" );
document.write( "curve gets closer and closer to these \r\n" );
document.write( "asymptotes but never touches them! \r\n" );
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document.write( "Edwin
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