We want to determine the sequence of transformations that were used to obtain the graph of $y = 3 (- x + 3)^{3}$ from the parent function $y = x^{3} .$ Let's first look at the graphs of the parent and the transformed functions.

We will start with the parent function $y = x^{3}$ and apply transformations one by one to obtain the given function. Let's begin by considering $y = (- x)^{3},$ which is a reflection across the $y -$ axis.

Now, let's take the graph of $y = (- x)^{3}$ and translate it $3$ units to the right. This is done by subtracting $3$ from the $x -$ variable. The resulting function after the translation is $y = (- (x - 3))^{3} .$

Before we continue, let's simplify the obtained function using the Distributive Property.

y = (- (x - 3))^{3} \Leftrightarrow y = (- x + 3)^{3}

Finally, we can stretch the graph of the function

y = (- x + 3)^{3}

by a factor of

3 .

This is done by multiplying the resulting function by

3 .

To summarize, we obtained the desired transformed function after a reflection of the parent function

y = x^{3}

across the

y -

axis, a shift

3

units to the right, and a stretch by a factor of

3 .

Therefore, the correct option is G.

Exercise

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