Even, odd and periodic functions

For even/odd tests the domain must be symmetric about 0. An even function satisfies f(-x)=f(x) for every permitted x; an odd function satisfies f(-x)=-f(x). **Type** | **Symmetry** | **Example** Even | About the y-axis | x2+1 Odd | Half-turn about the origin | x3-x Neither | Neither identity holds for all inputs | x2+x The zero function is both even and odd. Testing a few points can disprove a claimed identity but cannot prove it for every input. A periodic function repeats: f(x+T)=f(x) throughout its domain, which is preserved by the period. The least positive period, when it exists, is the fundamental period. For sin(3x), it is 2pi3.