2019 TYS

A function is defined as $\text{f}\left( x \right)=2{{x}^{3}}-6{{x}^{2}}+6x-12$.

1. Show that $\text{f}\left( x \right)$ can be written in the form $p\left\{ {{\left( x+q \right)}^{3}}+r \right\}$, where $p,q$ and $r$ are constants to be found.

   [2]

2. Hence, or otherwise, describe a sequence of transformations that transform the graph of $y={{x}^{3}}$ onto the graph of $y=\text{f}\left( x \right)$.

   [3]