Transformation of functions

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.

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

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

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

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

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

Use functions to create minimalist versions of works of art.