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Quartics

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

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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.

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Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Pitchfork

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Plot the graph of

$$x^y = y^x$$

in the first quadrant and explain its properties.