https://file.aiquickdraw.com/mathbot/file/1725516392424atj1qgpl.jpg

The function written in the image is:

\[
f(x) = \sqrt{x + 4} - 2
\]

This represents a square root function, where the expression inside the square root is \(x + 4\), and 2 is subtracted from the square root value.

### Domain:
For the square root function to be defined, the expression inside the square root must be non-negative:
\[
x + 4 \geq 0 \implies x \geq -4
\]
Thus, the domain of \(f(x)\) is \(x \geq -4\).

Would you like more details, or do you have any questions?

Here are 5 questions related to this concept:
1. What is the range of the function \( f(x) = \sqrt{x+4} - 2 \)?
2. How do we graph the function \( f(x) = \sqrt{x+4} - 2 \)?
3. How do transformations affect the function \( f(x) \)?
4. What happens to the domain if we modify the function to \( f(x) = \sqrt{x+4} + 2 \)?
5. Can you find the inverse of the function \( f(x) = \sqrt{x+4} - 2 \)?

**Tip:** When working with square roots, always remember that the value inside the root must be non-negative to avoid complex numbers.

Learn how to find the domain of the square root function f(x) = √(x + 4) - 2. Explore key algebraic concepts such as square root functions, transformations, and domain restrictions. Suitable for students in Grades 9-11.

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