document.write( "Question 1052647: Please, please help me graph this rational function $\"+g%28x%29=%28-5x%29%2F%28x%5E2-9%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "I already solve its intercepts, asymptotes and symmetry. I know how to graph the asymptotes but I don't know how to make a curve on this without passing through the asymptotes. \r
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Algebra.Com's Answer #667950 by josgarithmetic(39838) $\"\"$ $\"About$

You can put this solution on YOUR website!
Why? What happens NEAR the asymptotes? \r
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\n" ); document.write( "\n" ); document.write( "The best way to figure how to sketch a graph is to identify the critical x values. Those would be any zeros of g(x) and any vertical asymptotes. These cut the x-axis into intervals for you to check how g(x) behaves.\r
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document.write( "x value        significance\r\n" );
document.write( "-3             vertical asymptote\r\n" );
document.write( "0              root or zero\r\n" );
document.write( "3              vertical asymptote\r\n" );
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\n" ); document.write( "\n" ); document.write( "Next look at the signs for g in each interval on x. Pick any x value in each interval.
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document.write( "INTERVAL             pick x          sign of g\r\n" );
document.write( "(-infinity,-3)       -4              -5(-4)/((-4-3)(-4+3))=(+)/((-)(-))=POSITIVE\r\n" );
document.write( "(-3,0]               -1              -k(-1)/((-)(+))=NEGATIVE\r\n" );
document.write( "[0,3]                 1              -k(+)/((-)(+))=POSITIVE\r\n" );
document.write( "[3,infinity)          10             -k(+)/((+)(+))=NEGATIVE\r\n" );
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\n" ); document.write( "\n" ); document.write( "Think about g in those four intervals.
\n" ); document.write( "Starting very far from the left, approaching -3, g is positive, changing from very small to very large, and large without bound toward this asymptote.
\n" ); document.write( "Immediately to the right of this x=-3 asymptote, suddenly g is very large BUT NEGATIVE..., Do you see how this works? \r
\n" ); document.write( "\n" ); document.write( "Also notice change from negative to positive as g crosses the x-axis at 0.
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\n" ); document.write( "\n" ); document.write( " $\"graph%28400%2C400%2C-12%2C12%2C-12%2C12%2C-5x%2F%28x%5E2-9%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "The horizontal asymptote is y=0. \n" ); document.write( "

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