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Steve's Mapping

Age 16 to 18 Challenge Level:

Before starting to explore Steve's mapping, you might want to watch a short video explaining how to use the NRICH Number Plumber.
Steve has created two mappings which you can access by clicking on the picture below. The initial challenge is to figure out what Steve's mappings do. You can drop some numbers into the mappings, and see what comes out.

Test your ideas by predicting the outputs for some different inputs.
Only reveal the hidden parts of the mapping once you are certain you know what is going on.
Can you find an input which gives the same output for both mappings?

Click on the picture to explore Steve's mappings.

As you explore Steve's mappings, you will notice points appearing on the graph. The input number is the x coordinate, and the output number is the y coordinate.
Create some other function machines using the NRICH Number Plumber, and observe the outcomes on the graph.

Mathematicians like to ask themselves questions about what they notice.
What possible questions could you ask?

These questions may lead you to make conjectures - something which you believe to be true but need to investigate further in order to convince yourself.