tmua 2022 Q10

tmua · Uk · paper1 1 marks Function Transformations
A sequence of translations is applied to the graph of $y = x ^ { 3 }$
Which of the following graphs could be the result of this sequence of translations?
$$\begin{array} { l l } \text { I } & y = x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27 \\ \text { II } & y = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 3 \\ \text { III } & y = 27 x ^ { 3 } - 9 x ^ { 2 } + x - 3 \end{array}$$
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A sequence of translations is applied to the graph of $y = x ^ { 3 }$

Which of the following graphs could be the result of this sequence of translations?

$$\begin{array} { l l } 
\text { I } & y = x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27 \\
\text { II } & y = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 3 \\
\text { III } & y = 27 x ^ { 3 } - 9 x ^ { 2 } + x - 3
\end{array}$$