To solve this transformation problem, let's break down the given functions:

• $f(x) = (x - 2)^3$
• $g(x) = -(x + 2)^3$

We need to describe how to transform $f(x)$ into $g(x)$.

Step-by-step Transformation:

1. Shift the function horizontally:

   • The function $f(x) = (x - 2)^3$ is a cubic function that has been shifted right by 2 units (because of the $x - 2$).
   • To transform it into $g(x) = -(x + 2)^3$, we need to shift the graph left by 4 units (since $x + 2$ is the horizontal translation).

2. Reflection:

   • The negative sign in front of $(x + 2)^3$ indicates a reflection across the x-axis.

Thus, the correct transformation to get from $f(x)$ to $g(x)$ involves:

• Shifting the graph left by 4 units.
• Reflecting the graph across the x-axis.

Answer:

A. Translate left 4 units, and reflect across the x-axis to get $g(x)$.

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Let me know if you'd like more details or clarification. Here are a few related questions:

1. What are the general rules for translating and reflecting cubic functions?
2. How would the graph change if the reflection was across the y-axis instead?
3. What happens if we shift the function up or down instead of left or right?
4. How does the horizontal translation affect the overall behavior of cubic functions?
5. What is the impact of negative coefficients in polynomial functions?

Tip: When analyzing transformations, always focus on the order: horizontal shifts, reflections, and vertical shifts in that sequence.