Test each of the following for symmetry. Is f(x) even, odd, or neither?
a) f(x) = x³ + x² + x + 1
b) f(x) = 2x³ − 4x
a) $\displaystyle f(-x) = (-x)^3 + (-x)^2 + (-x) + 1 = -x^3 + x^2 - x + 1$
This result is neither f(x) nor is it -f(x). So this function is neither even, nor odd.
b)$\displaystyle f(-x) = 2(-x)^3 - 4(-x) = -2x^3 + 4x = -f(x)$
So this function is odd.