document.write( "Question 53515: List the intercepts and test for symmetry.
\n" ); document.write( "y = (x^2 - 5)/2x^3 \n" ); document.write( "

Algebra.Com's Answer #35776 by venugopalramana(3286) $\"\"$ $\"About$

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List the intercepts and test for symmetry.
\n" ); document.write( "y = (x^2 - 5)/2x^3
\n" ); document.write( "at x=0,we have y undefined...tends to infinity..hence the curve goes parallel to y axis approaching it at infinity as x tends to zero
\n" ); document.write( "at y=0,we have
\n" ); document.write( "x^2=5....x=+sqrt(5) and -sqrt(5) which are the x intercepts.
\n" ); document.write( "we find that by replacing x with -x and y with -y,we get same eqn.
\n" ); document.write( "-y = {(-x)^2-5}/2(-x)^3
\n" ); document.write( "y=(x^2-5)/2x^3 which is same eqn. as the given one.
\n" ); document.write( "hence the graph is symmetric about origin \n" ); document.write( "

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