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There are **13** NRICH Mathematical resources connected to **Transformation of functions**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### Tangled Trig Graphs

Can you work out the equations of the trig graphs I used to make my pattern?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Loch Ness

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Exploring Cubic Functions

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parabolas Again

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 14 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### The Why and How of Substitution

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.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Agile Algebra

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Painting by Functions

Use functions to create minimalist versions of works of art.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Operating Machines

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ellipses

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Parabolic Patterns

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

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 16 to 18

Challenge Level