Transformation of functions

There are 13 NRICH Mathematical resources connected to Transformation of functions
Sine Problem
problem

Sine Problem

Age
16 to 18
Challenge level
filled star empty star empty star
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.
Cubic Spin
problem

Cubic Spin

Age
16 to 18
Challenge level
filled star filled star empty star
Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?
The why and how of substitution
article

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.