Graph sketching

Sketch the graphs for this implicitly defined family of functions.

If you plot these graphs they may look the same, but are they?

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

What biological growth processes can you fit to these graphs?

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Can you match the charts of these functions to the charts of their integrals?