Q.10. 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?

I. $y = x^3 - 3x^2 + 9x - 27$
II. $y = x^3 - 9x^2 + 27x - 3$
III. $y = 27x^3 - 9x^2 + x - 3$

Answer Choices

• none of them
• I only
• II only
• III only
• I and II only
• I and III only
• II and III only
• I, II, and III

Solution

We analyze the given equations as potential translations of $y = x^3$. Each graph involves a combination of translations and possibly a scaling factor (in the case of III). Only option 2 can be the result of transformations applied to the original cubic graph. Therefore, the answer is II only.