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.
This pattern of graphs is the creation of Ali Abu-Hijleh, from Riccarton High School, Christchurch, New Zealand. Two of the equations are: $$y=(x+6)^3-2$$ $$y=-(x-9)^3+3$$
Find the equations of the other 12 graphs in this pattern.
You could use a graphic calculator or graphing software. For example, you can download Graphmatica for free from here and it comes with a good help file.
Draw your own pattern of graphs.