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Attractive Tablecloths

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Surprising Transformations

Age 14 to 16 Challenge Level:

This problem follows on from Translating Lines and Reflecting Lines.

I took the graph $y=4x+7$ and performed the four transformations shown on the cards below.

Transformation cards

Unfortunately, I can't remember the order in which I carried out the four transformations, but I know that I ended up with the graph of $y=4x-2$.

Can you find an order in which I could have carried out the transformations?
There is more than one way of doing this - can you find them all?
 
Can you explain why different orders can lead to the same outcome?

What other lines could I have ended up with if I had performed the four transformations in a different order?