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Mathematics-Online lexicon:

Symmetry to a Point and to a Line

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A function $ f(x)$ is symmetric to a vertical line $ x=a$ , $ a \in \mathbb{R}$ if

$\displaystyle f(a+x)=f(a-x). $

A function $ f(x)$ is symmetric to a point $ (b/f(b))$, $ b \in \mathbb{R}$ if

$\displaystyle f(b+x)-f(b)=-f(b-x)+f(b). $

(Authors: Jahn/Knödler)

see also:

[Examples]
  automatically generated 11/29/2004