Exercise 6 Page 899

We want to determine the sequence of transformations that were used to obtain the graph of $y=3(\text{-}x+3{)}^3$ 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 $y=(\text{-}x{)}^3,$ which is a reflection across the $y\text{-}$axis.

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

Before we continue, let's simplify the obtained function using the Distributive Property. Finally, we can stretch the graph of the function $y=(\text{-}x+3{)}^3$ 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 $y\text{-}$axis, a shift $3$ units to the right, and a stretch by a factor of $3.$ Therefore, the correct option is G.