Other changes to a graph

The graph of a function can be changed ("transformed") in ways other than the 'standard' transformations involving translations, reflections and dilations (stretching & shrinking).  Other changes to the graph of a function can involve the inclusion of absolute value (modulus) or taking the reciprocal - or a combination of the two.  The Geogebra applet below illustrates three of the more common 'non-standard' changes to the graph of the cubic function \(f\left( x \right) = 3x + \frac{{{x^2}}}{2} - \frac{{{x^3}}}{2}\).  You can enter a different function in the input box, if you wish.

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