Symmetry of Functions (Axial and Central Symmetry)

Axial symmetry: If f(a + x) = f(a - x), the graph is symmetric about the line x = a. Central symmetry: If f(a + x) + f(a - x) = 2b, the graph is symmetric abou…

Syllabus path: Functions › Concepts and Properties of Functions › Comprehensive Application of Function Properties

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CSCA Mathematics Formula Reference

Formula and explanation

Axial symmetry: If f(a + x) = f(a - x), the graph is symmetric about the line x = a. Central symmetry: If f(a + x) + f(a - x) = 2b, the graph is symmetric about the point (a, b). Special cases: Even and odd functions correspond to a = 0, b = 0.

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Comprehensive Application of Function Properties

Comprehensive Application of Function Properties 1. Core Concepts This section integrates all properties. Complex CSCA problems often combine Monotonicity, Parity, Periodicity, and Symmetry. Three Keys to Solving Problems: 1. Transformation: Use Parity/Periodicity to move the pro…

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