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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.

Witch of Agnesi

Stage: 5 Challenge Level: Challenge Level:1
Consider symmetry.
Find the critical values (turning points).
Consider what happens to the graphs for large $x$ (possitive and negative) and hence find the asymptote.