document.write( "Question 779331: What is the horizontal or oblique asymptotes, the vertical asymptotes, describe their meanings, for the following rational function:
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Algebra.Com's Answer #475218 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "f(x) = \r\n" );
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document.write( "The vertical asymptote is found by setting the denominator = 0\r\n" );
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document.write( "x+3 = 0\r\n" );
document.write( "  x = -3\r\n" );
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document.write( "That is the equation of a vertical line through -3 on the x axis.\r\n" );
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document.write( "So we draw that, in green:\r\n" );
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document.write( "Since the degree of the numerator, which is 2, is greater \r\n" );
document.write( "than the degree of the denominator, which is 1, there is \r\n" );
document.write( "no horizontal asymptote.\r\n" );
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document.write( "Since the degree of the numerator, which is 2, is exactly 1\r\n" );
document.write( "more than the degree of the denominator, which is 1, there \r\n" );
document.write( "is an oblique asymptote.\r\n" );
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document.write( "The equation of the oblique asymptote is found by dividing \r\n" );
document.write( "the denominator into the numerator by long division, \r\n" );
document.write( "ignoring the remainder, and setting y = the quotient:\r\n" );
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document.write( "        x-3\r\n" );
document.write( "x+3)x²+0x-5\r\n" );
document.write( "    x²+3x\r\n" );
document.write( "      -3x-5\r\n" );
document.write( "      -3x-9\r\n" );
document.write( "          4\r\n" );
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document.write( "So the oblique asymptote has the equation y = x-3.  \r\n" );
document.write( "It has intercepts (3,0) and (0,-3) So we draw that \r\n" );
document.write( "line (also in green):\r\n" );
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document.write( "Now we get some points (-7,-11), (-5,-10), (-4,-11), (-2,-1),\r\n" );
document.write( "(-1,-2),(0,), (1,-1), (3,), (5,)\r\n" );
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document.write( "  \r\n" );
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document.write( "Then draw in the graph through those points approacking the\r\n" );
document.write( "asymptotes:\r\n" );
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document.write( "Edwin

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