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The problem asks for a "3 unit moving of the function" \( g(x) = 12 - x^3 \). This likely refers to shifting the function either horizontally or vertically by 3 units.

- **Vertical shift**: Adding or subtracting a constant to the entire function shifts it up or down.
  - Shift up by 3: \( g(x) + 3 = (12 - x^3) + 3 = 15 - x^3 \)
  - Shift down by 3: \( g(x) - 3 = (12 - x^3) - 3 = 9 - x^3 \)

- **Horizontal shift**: Adjusting the input (inside the function's argument) moves the graph left or right.
  - Shift right by 3: \( g(x - 3) = 12 - (x - 3)^3 \)
  - Shift left by 3: \( g(x + 3) = 12 - (x + 3)^3 \)

Let me know if you'd like further clarification on one of these or another type of shift!

### Questions to consider:
1. Should the shift be vertical or horizontal in this context?
2. How does a vertical shift affect the shape of the graph compared to a horizontal one?
3. What happens to the intercepts when you shift the function up or down?
4. How would shifting the function to the left or right affect its turning points?
5. Can you explain how the general rule \( g(x \pm c) \) relates to horizontal shifts?

### Tip:
Remember, vertical shifts alter the function's output directly, while horizontal shifts change how the input \( x \) is transformed before applying the function's formula.

Find the 3 unit moving of the function g(x) = 12 - x^3.

Learn how to shift the cubic function g(x) = 12 - x^3 by 3 units. This problem covers vertical and horizontal shifts, explaining how to shift the graph of a cubic function up, down, left, or right by a given number of units. Suitable for students in Grades 9-12.

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