document.write( "Question 90849: 1) How do you determine the vertical asymptotes, given the equation of a rational function? \r
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\n" ); document.write( "\n" ); document.write( "3)If you let x take on very large positive values, and very small negative values, what can this tell you about the far right and left sides of the graph of a rational function that has a horizontal asymptote? \n" ); document.write( "
Algebra.Com's Answer #65919 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
1) How do you determine the vertical asymptotes, given the equation of a
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document.write( "Factor and simplify, canceling any like factors of numerator and denominator,\r\n" );
document.write( "then set the denominator = 0 and solve for x.  There will be a vertical\r\n" );
document.write( "asymptote at each of the values of x.   \r\n" );
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\n" ); document.write( "2) How do you determine the horizontal asymptotes, given the equation of a
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document.write( "By \"degree\" I mean the largest power of x that occurs.\r\n" );
document.write( "By \"leading coefficient\" I mean the coefficient of the largest power of x.\r\n" );
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document.write( "1. If the degree of the numerator is greater than the degree of the\r\n" );
document.write( "denominator, there is no horizontal asymptote.\r\n" );
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document.write( "2. If the degree of the numerator is equal to the degree of the denominator,\r\n" );
document.write( "then the horizontal asymptote is the horizontal line whose equation is\r\n" );
document.write( "y = (leading coefficient of numerator)/(leading coefficient of denominator)\r\n" );
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document.write( "3. If the degree of the numerator is less than the degree of the denominator,\r\n" );
document.write( "the horizontal asymptote is the x-axis, whose equation is y = 0.\r\n" );
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\n" ); document.write( "values, what can this tell you about the far right and left sides of the graph
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document.write( "Rule: This depends on the degree and the leading coefficient's sign. \r\n" );
document.write( "Always determine the graph's FAR RIGHT behavior FIRST.\r\n" );
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document.write( "GRAPH'S BEHAVIOR ON THE FAR RIGHT:\r\n" );
document.write( "If the leading coefficient is POSITIVE, then if you let x take on very large\r\n" );
document.write( "positive values, the graph's behavior on the far right is \"It eventually goes\r\n" );
document.write( "UPWARD on the far right\"\r\n" );
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document.write( "If the leading coefficient is NEGATIVE, then if you let x take on very large\r\n" );
document.write( "positive values, the graph's behavior on the far right is \"It eventually goes\r\n" );
document.write( "DOWNWARD on the far right\"\r\n" );
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document.write( "GRAPH'S BEHAVIOR ON THE FAR LEFT   \r\n" );
document.write( "If the degree is EVEN, if you let x take on very small negative values,\r\n" );
document.write( "then the graph's far left hand behavior is the SAME as the graph's far\r\n" );
document.write( "right hand-behavior.\r\n" );
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document.write( "If the degree is ODD, if you let x take on very small negative values,\r\n" );
document.write( "then the graph's far left hand behavior is OPPOSITE to the graph's far\r\n" );
document.write( "right hand-behavior.  \r\n" );
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document.write( "Edwin
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