NRICH: Surprising Transformations

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

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=4x2.

 

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?

Age 14 to 16


Algebra & Pre-Algebra, Functions & Graphs, Linear Equations
High School, Educator

What are you looking for?

Organization

NRICH (University of Cambridge)

Website URL

Type of Resource

Challenge

Assigned Categories