document.write( "Question 404617: what is the horizantal aymptotes of y=4/x-2+3 \n" ); document.write( "

Algebra.Com's Answer #286008 by richard1234(7193) $\"\"$ $\"About$

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The horizontal asymptotes of $\"y+=+4%2F%28x-2%29+%2B+3\"$ occur when $\"lim%28x-%3Einfinity%2C+4%2F%28x-2%29+%2B+3%29\"$ or $\"lim%28x-%3E-infinity%2C+4%2F%28x-2%29+%2B+4%29\"$ are defined (this is just the formal way of saying that when x gets really large, the value of y is a finite number).\r
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\n" ); document.write( "\n" ); document.write( "In this case, since the degree in the denominator is larger, $\"lim%28x-%3Einfinity%2C+4%2F%28x-2%29%29+=+0\"$ and $\"lim%28x-%3E-infinity%2C+4%2F%28x-2%29%29+=+0\"$ . Since the expression converges, we can add three to each limit and obtain 3 as our horizontal asymptotes. We can check by graphing the function, if we wish:\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C+4%2F%28x-2%29+%2B+3%2C+3%29\"$ \n" ); document.write( "

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