Transformation of functions

problem
Favourite

Parabolas Again

Age

14 to 18

Challenge level

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

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.
problem
Favourite

Exploring Cubic Functions

Age

14 to 18

Challenge level

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

Tangled Trig Graphs

Age

16 to 18

Challenge level

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

Loch Ness

Age

16 to 18

Challenge level

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

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.
problem

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.
problem

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.
problem

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?
problem

Painting by Functions

Age

16 to 18

Challenge level

Use functions to create minimalist versions of works of art.