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This problem developed from a question posed on the NRICH Projects site.

The mapping below was created using the NRICH Number Plumber.

Click here to watch a video explaining how to use the Number Plumber.

Click on the mapping to explore the relationship between the function and its graph.

(x-1)(x-3) mapping

Now replace the 1 and 3 with other values. How does this affect the graph?

What happens if you add instead of subtract?

Describe and explain any generalisations you make.