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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.