document.write( "Question 1127528: Determine algebraically whether the function f(x)=x^3-2x+1 is odd, even, or neither \n" ); document.write( "
Algebra.Com's Answer #743971 by greenestamps(13198)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The solution by mathlover1 is good, including descriptions of what makes a function even or odd.

\n" ); document.write( "For polynomial functions, the work is easier than what she shows.

\n" ); document.write( "The names \"even function\" and \"odd function\" come from the fact that any monomial function is even if the exponent is even and odd if the exponent is odd.

\n" ); document.write( "3 (the constant, exponent 0), x^2, x^4, and x^18 are even functions. That is easy to see, because replacing x with -x and raising to an even power gives the same result.

\n" ); document.write( "x, x^3, x^7, and x^73 are odd functions; again it is easy to see, because replacing x with -x and raising to an odd power gives the opposite result.

\n" ); document.write( "Then use the fact that a polynomial function is even or odd if and only if all the terms are either even or odd.

\n" ); document.write( "In the given function, the exponents on the variables are 3, 1, and 0. Since some are even and some are odd, the function is neither even nor odd.
\n" ); document.write( "
\n" );