document.write( "Question 205201: Hi all, I dont quite understand what this questions is asking:
\n" ); document.write( "Determine whether the following functions y = xsin3x, $\"y+=+x%2Asin%283x%29\"$ , $\"y+=+x%5E2+%2B+e%5Ex\"$ , $\"y+=+x%5E3%2Acosx\"$ are even, odd or none of these.
\n" ); document.write( "Can anyone help me with solving it and explain how to do it please?
\n" ); document.write( "Thanks, -Nick. \n" ); document.write( "

Algebra.Com's Answer #154910 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y+=+x%2Asin%283x%29\"$ , $\"y+=+x%5E2+%2B+e%5Ex\"$ , $\"y+=+x%5E3%2Acosx\"$
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document.write( "The graphs of even functions are symmetrical with respect to the\r\n" );
document.write( "y-axis.  Odd functions are symmetrical with respect to the origin.\r\n" );
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document.write( "There are two ways to show even, odd, or neither.  The first way is\r\n" );
document.write( "graphical. The second way is algebraic.  I'll do the graphical way\r\n" );
document.write( "first:\r\n" );
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document.write( "The graph of \r\n" );
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document.write( "It is symmetrical with respect to the y-axis, so it is an even function.\r\n" );
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document.write( "The graph of \r\n" );
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document.write( "It is not symmetrical with respect to the y-axis or with respect to the\r\n" );
document.write( "origin so it is neither even nor odd.\r\n" );
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document.write( "The graph of \r\n" );
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document.write( "It is symmetrical with respect to the origin, so it is odd.\r\n" );
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document.write( "How to tell algebraically whether the graph will be symmetrical\r\n" );
document.write( "with the y-axis (even), symmetrical with the origin (odd), or\r\n" );
document.write( "not symmetrical with respect to either the y-axis or the origin\r\n" );
document.write( "(neither):\r\n" );
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document.write( "Rules for the algebraic method:\r\n" );
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document.write( "Substitute -x for x and simplify.  If you get the same right side\r\n" );
document.write( "you started with after simplifying, the function is even.\r\n" );
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document.write( "If you get the original right side multiplied by -1, then the \r\n" );
document.write( "function is odd.\r\n" );
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document.write( "If you get neither, the function is neither even nor odd.\r\n" );
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document.write( "replace the x's by (-x)\r\n" );
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document.write( "Use the fact that \r\n" );
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document.write( "Two negatives make a positive\r\n" );
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document.write( "This is the same as the original right side so the\r\n" );
document.write( "function is even.\r\n" );
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document.write( " , \r\n" );
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document.write( "Replace the x's by (-x)\r\n" );
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document.write( "That is neither the same as the original right side,\r\n" );
document.write( "nor is it the original multiplied by -1,\r\n" );
document.write( "so it is neither an even nor an odd function.\r\n" );
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document.write( "Use the fact that \r\n" );
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document.write( "That is the original right side multiplied by -1, so\r\n" );
document.write( "the function is odd.\r\n" );
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document.write( "Edwin

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