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The question in your image asks to fill in the blanks to correctly complete the following sentence:

**"To obtain the graph of \( f(x) = (x + 8)^3 - 2 \), shift the graph of \( y = x^3 \) to the left \_\_ units and down \_\_ units."**

### Explanation:
The function \( f(x) = (x + 8)^3 - 2 \) is a transformation of the basic cubic function \( y = x^3 \). 

1. **Horizontal shift**: The term \( (x + 8) \) indicates a horizontal shift. Since it's \( x + 8 \), this means the graph shifts **8 units to the left** (opposite of the sign).
2. **Vertical shift**: The term \( - 2 \) outside the cubic function indicates a **vertical shift downward by 2 units**.

### Conclusion:
- **Left shift**: 8 units
- **Downward shift**: 2 units

So, the answer should be:
- Shift to the left **8 units**
- Shift down **2 units**

Would you like more details or have any other questions?

### 5 Related Questions:
1. How do you shift other types of functions horizontally or vertically?
2. What happens if the transformation inside the parentheses was \( x - 8 \)?
3. How does the general transformation of \( a(x + h)^n + k \) affect graphs?
4. What is the effect of a reflection on the graph of \( y = x^3 \)?
5. How do horizontal stretches and compressions affect the graph of a cubic function?

### Tip:
When analyzing transformations, always pay attention to the signs inside and outside the parentheses to determine the direction of shifts or reflections!

To obtain the graph of f(x) = (x + 8)^3 - 2, shift the graph of y = x^3 to the left __ units and down __ units.

Learn how to shift the graph of a cubic function y = x^3 horizontally and vertically. In this problem, we transform the function to f(x) = (x + 8)^3 - 2 by shifting it 8 units to the left and 2 units down. Suitable for students in Grades 9-12.

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