Simplifying Transformations

This problem is the third of three related problems.
The first two problems are Decoding Transformations and Combining Transformations .

There is also an article about the mathematics underlying these problems, called Grouping Transformations .

We have adopted the convention of listing a sequence of transformations from left to right; teachers may want to mention to their students that in other contexts a sequence of transformations may be listed from right to left.