Question

What is the Symmetry for F(x)=x^3? Odd Even or No Symmetry?

Answer 1

Examples of even functions (with symmetry about the y-axis:
constants, x^2, x^4, x^6, .... also cosine(x).
Sum and products of even functions are also even functions.

Examples of odd functions (with symmetry about the origin) :
x, x^3, x^5, x^7, .... and also sin(x).
Sums and products of odd functions are also odd functions.

Sum and products of mixed odd and even functions are neither odd nor even functions.