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CSCA MathematicsChapter 2: Functions, Derivatives & SequencesIntermediate

Function Properties: Monotonicity, Parity & Periodicity

函数的单调性、奇偶性与周期性 · Node 2.1

Domain symmetry, even/odd test $f(-x) = \pm f(x)$, strictly increasing/decreasing criteria, and periodic patterns $f(x+T) = f(x)$.

Chapter Weight: 35% of official examination
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Core Mathematical Axiom

Formula Proof & Traps
f(−x)=f(x)⟹Even,f(−x)=−f(x)⟹Odd,f(x+T)=f(x)
CSCA Exam Trap Alert

Assuming parity rules apply without verifying whether domain is symmetric about origin x = 0.

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