What the app does
f(−x) is compared with f(x) and with −f(x) at sample points across the domain: matching the first makes the function even, the second odd. A short list of candidate periods (π/2, π, 2π, 1, 2, 4) is then tested by shifting x and checking the values are unchanged.
Why it matters
Symmetry halves the work: an even or odd function only needs studying for x ≥ 0, and a periodic one only over a single period. It is also a strong check on everything else — the turning points of an odd function must come in mirrored pairs.
Read further
- Even and odd functions Wikipedia
- Periodic function Wikipedia
- Symmetry Paul's Online Notes