Transformation of functions

problem
Agile algebra

Age

16 to 18

Challenge level

Observe symmetries and engage the power of substitution to solve complicated equations.
problem
Painting by functions

Age

16 to 18

Challenge level

Use functions to create minimalist versions of works of art.
problem
Operating machines

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

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

Age

14 to 18

Challenge level

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