### Quartics

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

### Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

### Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

# Pitchfork

##### Age 16 to 18 Challenge Level:

Plot the graph of

$$x^y = y^x$$

in the first quadrant and explain its properties.