Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational
symmetry. Do graphs of all cubics have rotational symmetry?
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.
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.
Can you find the equations of the other twelve graphs in this pattern?
You may wish to use a graphical calculator or software such as Desmos to recreate the pattern for yourself.
This pattern of graphs was created by Ali Abu-Hijleh, from Riccarton High School, Christchurch, New Zealand.