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See what this second mathematical conclusion means.
Odd function's function image is symmetrical about the origin center in rectangular coordinate system.

Even function images are symmetric about y.

For conclusion 1. If the domain contains 0, the function image must pass through the origin (0,0).

As for conclusion 2, he wrote the conclusion in the front, so it was awkward.

Odd function if and only if a0=a2=0.

It is an even function if and only if a 1=a3=0.