Composition of Transformations
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When two or more transformations are combined to form a new transformation, the result is called a composition of transformations.  In a composition, the first transformation produces an image upon which the second transformation is then performed. 

The symbol for a composition of transformations is an open circle. 
The notation is read as a reflection in the x-axis following a translation of
(x+3, y+4).  Be careful!!!  The process is done in reverse!!

 

You may see various notations which represent a composition of transformations:
  could also be indicated by 

 

Renaming a composition:  It is possible that a composition of two transformations may be renamed by only one other transformational method.  For example, the composition of a line reflection in the y-axis followed by a line reflection in the x-axis could be described as a single transformation of a reflection in the origin.