Transformation of functions

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

Use functions to create minimalist versions of works of art.

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

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.

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

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

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

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.

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.