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Cubic Spin

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

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.

Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

More Parabolic Patterns

Age 14 to 18
Challenge Level

This is another inverse problem. If you were given the equations and asked to draw the graphs then graphing software would do the work for you. This challenge is posed the opposite way round. You have to use mathematical reasoning to deduce the equations of the graphs in the illustration. Then you can use graphing software to check to see if your reasoning was correct.