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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.

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

If you draw the graph using graphing software then you must still explain how you could predict all the features of the graph from the equation. You may like to download the free graphing shareware package Graphmatica.