document.write( "Question 389527: What is the slant asymptote for the function f(x)=(3x^2-4x+3)/(x+2)? \n" ); document.write( "

Algebra.Com's Answer #276027 by Edwin McCravy(20060) $\"\"$ $\"About$

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What is the slant asymptote for the function f(x)=(3x^2-4x+3)/(x+2)?\r
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document.write( "Rewrite the function by dividing out the expression on the right\r\n" );
document.write( "by long division:\r\n" );
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document.write( "            3x - 10\r\n" );
document.write( "x + 2)3x² - 4x +  3\r\n" );
document.write( "      3x² + 6x\r\n" );
document.write( "          -10x +  3\r\n" );
document.write( "          -10x - 20\r\n" );
document.write( "                 23\r\n" );
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document.write( "  \r\n" );
document.write( "That red fraction becomes very small when x is very large in absolute\r\n" );
document.write( "value.  For instance when x = 1000000, the red fraction \r\n" );
document.write( "becomes  becomes .0000223 which is very near zero.  And also,\r\n" );
document.write( "when x = -1000000, the red fraction  becomes -.000023 which is very near zero.\r\n" );
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document.write( "That means\r\n" );
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document.write( "gets closer and closer to just being equal to the green part:\r\n" );
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document.write( "Here is the graph:. The green line is the slant asymptote, whose\r\n" );
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document.write( "equation is\r\n" );
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document.write( "y = 3x - 10\r\n" );
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document.write( "Edwin

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