Transformation of functions

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

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
problem
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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?

Loch Ness
problem
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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
Favourite

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?

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.
More Parabolic Patterns
problem

More parabolic patterns

Age
14 to 18
Challenge level
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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.
Ellipses
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Ellipses

Age
14 to 18
Challenge level
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Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.
Operating machines
problem

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?