It is given that $\mathrm{f}\left( x \right)={{\left( 1-2x \right)}^{3}}-2$ is the final grap

Question

It is given that $\mathrm{f}\left( x \right)={{\left( 1-2x \right)}^{3}}-2$ is the final graph after $\mathrm{g}\left( x \right)={{x}^{3}}$ undergoes exactly $4$ transformations. Describe the transformations involved and state the coordinates in which $\left( 0,0 \right)$ is mapped onto the graph of $\mathrm{f}\left( x \right)$.

Accepted Answer

One valid sequence is a scaling by factor $\dfrac12$ parallel to the $x$-axis, reflection in the $y$-axis, translation $\dfrac12$ unit in the positive $x$-direction, and translation $2$ units in the negative $y$-direction. The point $(0,0)$ maps to $\left(\dfrac12,-2\right)$.

Transformations of Graphs - Composite Transformations

Transformations of Graphs - Composite Transformations

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