document.write( "Question 1131911: Use limits to describe the behavior of the rational function near the indicated asymptote.
\n" ); document.write( " f(x) = (4x^2 - 3)/(x^2 + 1)
\n" ); document.write( "Describe the behavior of the function near its horizontal asymptote (the end behavior) \n" ); document.write( "

Algebra.Com's Answer #748646 by MathLover1(20849) $\"\"$ $\"About$

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$\"lim%28x-%3Einfinity%29\"$ $\"+%284+x%5E2+-+3%29%2F%28x%5E2+%2B+1%29+=+4\"$ \r
\n" ); document.write( "\n" ); document.write( "A horizontal asymptote is\r
\n" ); document.write( "\n" ); document.write( " $\"%284+x%5E2+-+3%29%2F%28x%5E2+%2B+1%29\"$ -> $\"4\"$ as $\"x\"$ -> ą $\"infinity\"$ \r
\n" ); document.write( "\n" ); document.write( "A horizontal asymptote is in this case a horizontal line $\"y=4\"$ that indicates where a function flattens out as $\"x\"$ gets very large or very small. A function may touch or pass through a horizontal asymptote. \r
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\n" ); document.write( "\n" ); document.write( " $\"Image$ \r
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\n" ); document.write( "\n" ); document.write( "as you can see on the graph, a function didn't touch or pass through a horizontal asymptote\r
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