document.write( "Question 910574: Do I have this correct?
\n" ); document.write( "consider the rational function:
\n" ); document.write( "\"+f%28x%29+=+12%2F%28x-2%29%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "x-intercept: numerator set to zero, therefore (-12,0) \r
\n" ); document.write( "\n" ); document.write( "y-intercept: all x's set to zero, therefore (0,12) \r
\n" ); document.write( "\n" ); document.write( "Vertical Asymptote: set denominator to zero to find restraints, therefore -2,2 would it be both? \r
\n" ); document.write( "\n" ); document.write( "Horizontal Asymptote: compare degrees 12x^0/x^2 so y=0 or none. \r
\n" ); document.write( "\n" ); document.write( "Do I have this correct? please describe what I have correct or incorrect in my reasoning. \r
\n" ); document.write( "\n" ); document.write( "Thank you
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Algebra.Com's Answer #552559 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Do I have this correct?
\n" ); document.write( "consider the rational function:
\n" ); document.write( "\"+f%28x%29+=+12%2F%28x-2%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "x-intercept: numerator set to zero, therefore (-12,0)
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document.write( "No, the numerator is 12.  You cannot set 12 equal to 0.\r\n" );
document.write( "12 is always 12, never 0.  So there is no x-intercept.\r\n" );
document.write( "The graph does not intersect the x-axis.\r\n" );
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\n" ); document.write( "y-intercept: all x's set to zero, therefore (0,12)
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document.write( "No.  To set x=0 means to replace x by 0.\r\n" );
document.write( "\"+%22f%28x%29%22+=+12%2F%28x-2%29%5E2\"\r\n" );
document.write( "\"+%22f%280%29%22+=+12%2F-2%29%5E2\"\r\n" );
document.write( "\"+%22f%280%29%22+=+12%2F4\"\r\n" );
document.write( "\"+%22f%280%29%22+=+3\" \r\n" );
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\n" ); document.write( "Vertical Asymptote: set denominator to zero to find restraints, therefore -2,2 would it be both?
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\r\n" );
document.write( "No, \r\n" );
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document.write( "\"%28x-2%29%5E2=0\"\r\n" );
document.write( "Take square roots of both sides:\r\n" );
document.write( "\"x-2=+%22%22+%2B-+0\"\r\n" );
document.write( "\"x-2=0\"\r\n" );
document.write( "\"x=2\"\r\n" );
document.write( "It's the 0 that ± not the 2. When 0 is ±, it's just at x=0. \r\n" );
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\n" ); document.write( "Horizontal Asymptote: compare degrees 12x^0/x^2 so y=0 or \"cross%28none%29\".
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\r\n" );
document.write( "No y=0 MEANS the x-axis is the horizontal asymptote, not \"none\". \r\n" );
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document.write( "Here is the graph, gotten by plotting and connecting points\r\n" );
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document.write( "(-8,.12),(-6,.1875), (-4,.333), (-3,.48), (-2,.75), (-1,1.333), (0,3), (1,12),\r\n" );
document.write( "(3,12), (4,3), (5, 1.333), (6,.75), (7,.48), (8,.333), (10,.1875), (12,.12)\r\n" );
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document.write( " \r\n" );
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document.write( "Notice that it does not cross the x-axis, has y-intercept (0,3), \r\n" );
document.write( "has green vertical asymptote at x=2, and horizontal asymptote which\r\n" );
document.write( "is the x-axis, whose equation is y=0.\r\n" );
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document.write( "Edwin
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