document.write( "Question 1129484: Which characteristic is correct for the function f(x)=-6x^5+4x^3 ?\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "both even and odd\r
\n" ); document.write( "\n" ); document.write( "even\r
\n" ); document.write( "\n" ); document.write( "neither even nor odd\r
\n" ); document.write( "\n" ); document.write( "odd \n" ); document.write( "
Algebra.Com's Answer #746385 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Which characteristic is correct for the function f(x)=-6x^5+4x^3 ?
\n" ); document.write( "
\r\n" );
document.write( "First we do it visually.\r\n" );
document.write( "If it is symmetrical with respect to the y-axis, it is even.\r\n" );
document.write( "If it is symmetrical with respect to the origin, it is odd.\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-1.3%2C1.3%2C-1.3%2C1.3%2C-6x%5E5%2B4x%5E3%29\"\r\n" );
document.write( "\r\n" );
document.write( "It's symmetrical with respect to the origin so it's an ODD function.\r\n" );
document.write( "\r\n" );
document.write( "Next we do it algebraically:\r\n" );
document.write( "\r\n" );
document.write( "It is even if f(-x) = f(x)\r\n" );
document.write( "It is odd if f(-x) = -f(x)\r\n" );
document.write( "\r\n" );
document.write( "f(x) = -6x5+4x3\r\n" );
document.write( "f(-x) = -6(-x)5+4(-x)3\r\n" );
document.write( "f(-x) = -6(-x5)+4(-x3)\r\n" );
document.write( "f(-x) = 6x5-4x3\r\n" );
document.write( "f(-x) = -(6x5+4x3)\r\n" );
document.write( "f(-x) = -f(x)\r\n" );
document.write( "\r\n" );
document.write( "The function is odd.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );