document.write( "Question 635571: how do you identify asymptotes? \n" ); document.write( "

Algebra.Com's Answer #400415 by MathLover1(20850) $\"\"$ $\"About$

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Veritcal asymptotes are where the denominator of a fraction becomes $\"0\"$ and \r
\n" ); document.write( "\n" ); document.write( "the value of $\"f%28x%29\"$ becomes $\"undefined\"$ . Set the $\"denominator\"$ to \r
\n" ); document.write( "\n" ); document.write( " $\"0\"$ and solve.\r
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\n" ); document.write( "\n" ); document.write( "Horizontal asymptotes are values of $\"f%28x%29\"$ when $\"x\"$ → $\"infinity\"$ \r
\n" ); document.write( "\n" ); document.write( " and $\"x\"$ → $\"-infinity\"$ \r
\n" ); document.write( "\n" ); document.write( "here is example:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x%5E2+%2F+%28x%5E2%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Vertical asymptote:\r
\n" ); document.write( "\n" ); document.write( "Set $\"+%28x%5E2%2B1%29=0\"$ and solve for $\"x\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"+x%5E2=-1\"$ has $\"+no\"$ real solution, so there is $\"no\"$ $\"vertical\"$ $\"+asymptote\"$ .\r
\n" ); document.write( "\n" ); document.write( "Horizontal:
\n" ); document.write( "Divide all terms by the highest power of $\"x\"$ to eliminate unimportant values\r
\n" ); document.write( "\n" ); document.write( "dividing by $\"x%5E2\"$ , you get $\"3+%2F+%281+%2B+%281%2Fx%5E2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "As $\"x\"$ → $\"infinity\"$ then $\"1%2Fx%5E2\"$ → $\"0\"$ (it vanishes), \r
\n" ); document.write( "\n" ); document.write( "leaving $\"3%2F1=3\"$ , so there is a horizontal asymptote at $\"y=3\"$ \r
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