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. ** **