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The function given is:

\[
f(x) = \sqrt{x - 3} - 3
\]

### **Finding the Domain**
Since the function contains a square root, the expression inside the square root \(x - 3\) must be **non-negative** (greater than or equal to 0). 

\[
x - 3 \geq 0
\]

\[
x \geq 3
\]

Thus, the **domain** of the function is all real numbers \(x\) such that \(x \geq 3\).

### **Domain in Interval Notation:**
\[
[3, \infty)
\]

This means the function is only defined for values starting from \(x = 3\) and going to infinity.

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### **Related Questions:**
1. What is the range of the function \(f(x) = \sqrt{x - 3} - 3\)?
2. How do square root functions behave for negative inputs?
3. How do you determine domain for more complex functions with multiple constraints?
4. What changes if the function were \(f(x) = \sqrt{3 - x} - 3\)?
5. How does a graphing calculator verify the domain of a function?

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**Tip:** When working with square roots, always start by ensuring the expression inside the radical is non-negative to find the domain.

Use graphing technology to find the domain of the function f(x) = √(x - 3) - 3.

Explore how to determine the domain of the function f(x) = √(x - 3) - 3 using graphing technology. This step-by-step explanation focuses on square root properties and finding domain constraints. Suitable for students in Grades 9-12.

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