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Functions and Graphs - Stage 3

Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Khun Phaen Escapes to Freedom

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Frieze Patterns in Cast Iron

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

Surprising Transformations

Stage: 3 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?

Reflections. Possible Roadshow. Linear functions. Rotations. Translations. Cartesian equations of lines. Graphs. collaborative. Symmetry. Gradients.