document.write( "Question 390262: My son is struggling with these graphing rational functions. Can anyone help?\r
\n" ); document.write( "\n" ); document.write( "1. How do I graph f(x)=(6x+5)/(2x+8)?\r
\n" ); document.write( "\n" ); document.write( "2. How do I graph f(x)=(x+3)/(x^2-25)? \n" ); document.write( "

Algebra.Com's Answer #276681 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. How do I graph $\"%22f%28x%29%22=%286x%2B5%29%2F%282x%2B8%29\"$ ?
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document.write( "First find the vertical asymptote by setting the denominator = 0:\r\n" );
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document.write( "2x + 8 = 0\r\n" );
document.write( "    2x = -8\r\n" );
document.write( "     x = -4\r\n" );
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document.write( "That is the equation of a vertical line through -4 on the x-axis:\r\n" );
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document.write( "Next find the horizontal asymptote by this rule, when the degree\r\n" );
document.write( "(largest exponent of x in the numerator) is equal to the degree (largest\r\n" );
document.write( "exponent of x in the denominator)\r\n" );
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document.write( "and simplify:\r\n" );
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document.write( "y = 3\r\n" );
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document.write( " That is the equation of a horizontal line through 3 on the y-axis:\r\n" );
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document.write( "Next get some points on the graph, getting some on the left\r\n" );
document.write( "of the vertical asymptotes and some on the right:\r\n" );
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document.write( "  x | y\r\n" );
document.write( "-14 |  3.95\r\n" );
document.write( " -9 |  4.9\r\n" );
document.write( " -6 |  7.75\r\n" );
document.write( " -5 | 12.5\r\n" );
document.write( " -3 | -6.5\r\n" );
document.write( " -2 | -1.75\r\n" );
document.write( "  0 |   .625\r\n" );
document.write( "  1 | 1.1\r\n" );
document.write( "  6 | 2.05\r\n" );
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document.write( "Then sketch in the curve:\r\n" );
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document.write( "2. How do I graph f(x)=(x+3)/(x^2-25)?\r\n" );
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document.write( "First find the vertical asymptote by setting the denominator = 0:\r\n" );
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document.write( "       x² - 25 = 0\r\n" );
document.write( "(x - 5)(x + 5) = 0\r\n" );
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document.write( "x - 5 = 0;  x + 5 = 0\r\n" );
document.write( "    x = 5       x = -5\r\n" );
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document.write( "Those is the equation of vertical lines through 5 and -5 on the x-axis:\r\n" );
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document.write( "Next find the horizontal asymptote by this rule, when the degree of the\r\n" );
document.write( "numerator is less than the dgree of the numerator. The horizontal is the\r\n" );
document.write( "x-axis, the line whose equation is\r\n" );
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document.write( "That is the equation of a horizontal line which is the x-axis:\r\n" );
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document.write( "Next get some points on the graph, getting some on the left\r\n" );
document.write( "and right of each vertical asymptote. In this one you should\r\n" );
document.write( "get some points real near the asymptotes, at -5.1, -4.9, and 4.9,5.1\r\n" );
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document.write( "  x |  y\r\n" );
document.write( "-10 |  -.09\r\n" );
document.write( " -6 |  -.27\r\n" );
document.write( "-5.1| -2.08 \r\n" );
document.write( "-5  | no value (asymptote)\r\n" );
document.write( "-4.9|  1.91\r\n" );
document.write( " -4 | -0.11\r\n" );
document.write( " -3 |  0\r\n" );
document.write( " -1 | -0.08 \r\n" );
document.write( "  0 | -0.12\r\n" );
document.write( "  1 | -0.167\r\n" );
document.write( "  3 | -0.375\r\n" );
document.write( "  4 | -0.778\r\n" );
document.write( " 4.9| -7.98 \r\n" );
document.write( "  5 | no value (asymptote)\r\n" );
document.write( " 5.1|  8.02 \r\n" );
document.write( "  6 | .82\r\n" );
document.write( "  9 | .21 \r\n" );
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document.write( "Then sketch in the curve:\r\n" );
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document.write( "Edwin

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