Homework Help: odd and even functions

Posted by Jen on Tuesday, January 30, 2007 at 2:04pm.

Using f is odd if f(-x) = -f(x) or even if f(-x) = f(x) for all real x, how do I
1)show that a polynomial P(x) that contains only odd powers of x is an odd function
2)show that if a polynomial P(x) contains both odd and even powders of x, then it is neither an odd nor an even function
Thanks in advance

You have the definition, so put -x in for x and see if it matches the odd or even definition. To be odd, all the terms have to change.

For instance f(x)= x + 3

That is not odd,nor even, because f(2)=5, and f(-2)=2, using your definitions

So to write the answer, I just use examples and prove it?

Thanks

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