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The illustration below shows the graphs of fourteen functions.
Two of them have equations $$y=(x+6)^3-2$$ $$y=-(x-9)^3+3$$

graph.


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.