Is x^3 - x + 1 an Even, Odd, or Neither Function?

[Caldus]

Is the function x^3 - x + 1 even, odd, or neither? When I graphed this, it looked like it was symmetric about the origin, so I thought that it might be an odd function. Either that or it is neither?

 

[cookiemonster]

A function is even if:

f(-x) = f(x)

A function is odd if:

f(-x) = -f(x)

So to figure out if it's even of odd, plug in -x in place of x and compare it to the original.

cookiemonster

 

[Tom McCurdy]

Look at graph

Also I believe that odd fuctions are rotationaly symetric while even fuctions are symetic on the vertical line. (When a graph is fliped horizontally over it)

 

[matt grime]

f(0) isn' 0 so it certainly isn't odd, and clearly it isn't even.

hint: a polynomial in x is even (odd) iff the powers of x are all even (odd)