Transformation of functions

There are 13 NRICH Mathematical resources connected to Transformation of functions
Loch Ness
problem
Favourite

Loch ness

Age
16 to 18
Challenge level
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Draw graphs of the sine and modulus functions and explain the humps.
Tangled Trig Graphs
problem
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Tangled trig graphs

Age
16 to 18
Challenge level
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Can you work out the equations of the trig graphs I used to make my pattern?

Parabolic Patterns
problem
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Parabolic patterns

Age
14 to 18
Challenge level
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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.

Parabolas Again
problem
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Parabolas again

Age
14 to 18
Challenge level
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Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
Exploring cubic functions
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Exploring cubic functions

Age
14 to 18
Challenge level
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Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Operating machines
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Operating machines

Age
16 to 18
Challenge level
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What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Painting by functions
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Painting by functions

Age
16 to 18
Challenge level
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Use functions to create minimalist versions of works of art.
Agile Algebra
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Agile algebra

Age
16 to 18
Challenge level
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Observe symmetries and engage the power of substitution to solve complicated equations.

Cubic Spin
problem

Cubic spin

Age
16 to 18
Challenge level
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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
problem

Sine problem

Age
16 to 18
Challenge level
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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.