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Surprising Transformations

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?



The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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