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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?

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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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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.

Agile Algebra

Stage: 5 Challenge Level: Challenge Level:1

(1) Divide top and bottom of fractions by $x$ and substitute $X=2x + \frac{3}{x}.$

(2) Divide by $x^2$and substitute $X=x + \frac{1}{x}.$

(3) Combine brackets 1 and 4 and brackets 2 and 3.

(4) Substitute $X = 8x + 7$.