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To make the function \( f(x) = (x + 3)^2 \) one-to-one and still maintain the same range, we need to restrict its domain. 

The function \( f(x) = (x + 3)^2 \) is a parabola that opens upward, with its vertex at \( x = -3 \). The function is symmetric around this vertex, so if we choose a domain where \( x \geq -3 \), the function will increase from its minimum point without repeating any values, making it one-to-one. 

### Solution:
To make \( f(x) \) one-to-one:
- **Restrict the domain to** \( x \geq -3 \).

This restriction ensures the function remains increasing from \( x = -3 \) onward, thus maintaining a unique output for each input.

Would you like more details on this process or have any questions?

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Here are 5 questions that extend this concept:
1. Why does restricting the domain to \( x \geq -3 \) make the function one-to-one?
2. How would the range of the function be affected if we used \( x \leq -3 \) instead?
3. What other types of functions require domain restrictions to be one-to-one?
4. How does the concept of an inverse function relate to making a function one-to-one?
5. Could we use any other value besides \( x = -3 \) to split the domain and make the function one-to-one?

**Tip:** For parabolas, restricting the domain to one side of the vertex (either left or right) is a common way to make the function one-to-one.

How would you limit the domain to make the function one-to-one and still have the same range?

Learn how to restrict the domain of the quadratic function f(x) = (x + 3)^2 to make it one-to-one while maintaining the same range. This solution covers key algebraic concepts, including domain restriction and one-to-one functions, suitable for high school students.

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