As I couldn't find a nice example for anti-periodic functions... I publish this as an example.
Anti-Periodic: f(x+P)= - f(x) , P is periodocity
One easy choice is to , chose a function with no lesser periodicity than 2P and it's second Half [P,2P] should be a shift of first Half [0,P] of the function with inversion / mirrored.
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