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.







Now replace the 2 and 3 with other values. How does this affect the graph?

What happens when you try division instead of multiplication, or subtraction instead of addition?



Describe and explain any generalisations you make.