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Broad Topics >

Advanced Algebra > Transformation of functions

##### Age 14 to 18 Challenge Level:

The illustration shows the graphs of twelve functions. Three of
them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations
of all the other graphs.

##### Age 14 to 18 Challenge Level:

Knowing two of the equations find the equations of the 12 graphs of
cubic functions making this pattern.

##### Age 14 to 18 Challenge Level:

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.

##### Age 14 to 18 Challenge Level:

Here is a pattern composed of the graphs of 14 parabolas. Can you
find their equations?

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Use functions to create minimalist versions of works of art.

##### Age 16 to 18 Challenge Level:

Observe symmetries and engage the power of substitution to solve
complicated equations.

##### Age 14 to 18 Challenge Level:

Here is a pattern for you to experiment with using graph drawing
software. Find the equations of the graphs in the pattern.

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

Draw graphs of the sine and modulus functions and explain the
humps.

##### Age 16 to 18 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?