document.write( "Question 134844: Identify all asymptotes and holes in the graph of the following rational function:\r
\n" ); document.write( "\n" ); document.write( "f(x) = ((2x^3+6x^2)/(x^2-x-12)) \n" ); document.write( "

Algebra.Com's Answer #98686 by vleith(2983) $\"\"$ $\"About$

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Asymptotes occur when the denominator is zero. \r
\n" ); document.write( "\n" ); document.write( "So what values of x make the denominator 0?
\n" ); document.write( " $\"%28x%5E2-x-12%29+=+0\"$
\n" ); document.write( " $\"%28x-4%29%28x%2B3%29+=+0\"$
\n" ); document.write( "x = 4, x =-3\r
\n" ); document.write( "\n" ); document.write( "asymptotes are the lines x=4 and x=-3\r
\n" ); document.write( "\n" ); document.write( "Holes occur when both the numerator and denominator are 0.
\n" ); document.write( " $\"%28%282x%5E3%2B6x%5E2%29%2F%28x%5E2-x-12%29%29\"$
\n" ); document.write( " $\"+%282x%5E2%28x%2B3%29%29%2F+%28%28x-4%29%28x%2B3%29%29\"$
\n" ); document.write( "So we have a hole at x = -3 \n" ); document.write( "

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