Function Symmetric about the Line x = a
If the graph of the function f(x) is symmetric about the line x = a, then for any x in its domain, we have f(a + x) = f(a - x). Equivalently, f(x) = f(2a - x).
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 line x = a, then for any x in its domain, we have f(a + x) = f(a - x). Equivalently, f(x) = f(2a - x).
Related tutorial and examples
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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