Function Symmetric about the Point (a, b)

If the graph of the function f(x) is symmetric about the point (a, b), then for any x in its domain, we have f(a + x) + f(a - x) = 2b. Equivalently, f(x) + f(2…

Syllabus path: Functions › Concepts and Properties of Functions › Symmetry of Functions

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CSCA Mathematics Formula Reference

Formula and explanation

If the graph of the function f(x) is symmetric about the point (a, b), then for any x in its domain, we have f(a + x) + f(a - x) = 2b. Equivalently, f(x) + f(2a - x) = 2b.

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Symmetry of Functions

Symmetry of Functions 1. Concept Symmetry describes the mirroring or rotational relationship of a function's graph. Axial Symmetry (Reflection): The graph is symmetric about a vertical line x = a. (e.g., Even functions correspond to the axis x = 0 ). Central Symmetry (Rotation): …

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