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Resources tagged with Transformation of functions similar to Small Steps:

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Broad Topics > Advanced Algebra > Transformation of functions

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Ellipses

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.

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Parabolas Again

Age 14 to 18 Challenge Level:

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

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Cubics

Age 14 to 18 Challenge Level:

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

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Cubic Spin

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?

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More Parabolic Patterns

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.

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The Why and How of Substitution

Age 16 to 18

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

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Parabolic Patterns

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.

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Sine Problem

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.

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Loch Ness

Age 16 to 18 Challenge Level:

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

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Painting by Functions

Age 16 to 18 Challenge Level:

Use functions to create minimalist versions of works of art.

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Agile Algebra

Age 16 to 18 Challenge Level:

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

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Operating Machines

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?