document.write( "Question 825188: Identify the vertical asymptotes for each equation State the domain for each equation.
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Algebra.Com's Answer #497142 by math-vortex(648) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Hi, there--\r\n" );
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document.write( "PROBLEM:\r\n" );
document.write( "Identify the vertical asymptotes for each equation. State the domain.\r\n" );
document.write( "a) \r\n" );
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document.write( "b) \r\n" );
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document.write( "SOLUTION:\r\n" );
document.write( "Consider the first equation:\r\n" );
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document.write( "We typically have restrictions on the domain of a function for two reasons: taking the square \r\n" );
document.write( "root of a negative number, and division by zero. There are no square roots in this equation, \r\n" );
document.write( "but we are dividing by a polynomial. We need to find any value of x for which the denominator \r\n" );
document.write( "will equal 0 to avoid division by zero (a big no-no!)\r\n" );
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document.write( "Find the zeroes (roots) for the polynomial in the denominator. Set the denominator equal to \r\n" );
document.write( "zero and solve for x.\r\n" );
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document.write( " or \r\n" );
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document.write( "In order to avoid division by zero, we restrict our domain to all the real numbers except -2 \r\n" );
document.write( "and 2. \r\n" );
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document.write( "Domain: all the real numbers, such that  or \r\n" );
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document.write( "In bracket notation (using a \"sideways 8\" for infinity):\r\n" );
document.write( "Domain: (-infinity,-2) U (-2,2) U (2, infinity)\r\n" );
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document.write( "Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a \r\n" );
document.write( "rational function. We have already found the zeros for the denominator of this function:\r\n" );
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document.write( "Vertical Asymptotes:  and \r\n" );
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document.write( "I will leave the second equation for you to work out on your own. Feel free to email me at the \r\n" );
document.write( "address below if you get stuck or want to check your answers.\r\n" );
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document.write( "Good luck!\r\n" );
document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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