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The functions  ,  , given by  ,  ,  ,  ,  , and  form a group with the composition of maps; for instance  . Moreover, if we take  , we have  ,  , that is, the function  is invariant with respect to the group of transformations  . The graph demonstrates this behaviour: choose a real number  on the horizontal axis; the numbers  ,  are shown on the same axis and the corresponding values  (red points) are all at the same height. |
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