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 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.

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 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.