document.write( "Question 303223: What are the zeros and asymptotes of $\"y+=+%28x%5E2-3x%29%2F%28x%2B4%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #217322 by Edwin McCravy(20065) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "To find the zeros, we set the rational function equal to 0:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the graph crosses the x-axis at 0 and 3:\r\n" );
document.write( "\r\n" );
document.write( "To find the vertical asymptote(s), we set the denominator\r\n" );
document.write( "equal to zero:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That is the equation of a vertical line through 4 on the x-axis:\r\n" );
document.write( "\r\n" );
document.write( "Since the degree of the numerator  is 2 and the degree\r\n" );
document.write( "of the denominator is 1, the numerator has a greater degree so this\r\n" );
document.write( "rational function cannot have a horizontal asymptote.  However since\r\n" );
document.write( "the degree of the numerator is exactly 1 degree greater than the \r\n" );
document.write( "denominator, there is a slanted or oblique asymptote which we find \r\n" );
document.write( "by long division:\r\n" );
document.write( "\r\n" );
document.write( "             x -  7  \r\n" );
document.write( "x + 4)x² -  3x +  0\r\n" );
document.write( "      x² + 4x\r\n" );
document.write( "           -7x +  0\r\n" );
document.write( "           -7x - 28\r\n" );
document.write( "                 28\r\n" );
document.write( "\r\n" );
document.write( "We ignore the remainder and the slanted or oblique asymptote\r\n" );
document.write( "is the line whose equation is . Drawing in the\r\n" );
document.write( "two asymptotes in green and the graph in red, we have:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   \r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );