https://file.aiquickdraw.com/mathbot/file/1732164713224chrfhepm.jpg

To address this problem, let’s break it down:

The given function is:

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

The instructions suggest starting with the basic square root function:

\[
g(x) = \sqrt{x}
\]

### Transformations:
1. The "+4" inside the square root shifts the graph **horizontally to the left** by 4 units. This is because adding to \(x\) inside a function shifts the graph in the opposite direction (left) compared to subtraction.

So the final answer is:

- Start with the graph of \(g(x) = \sqrt{x}\), then shift it **4 units left**.

Would you like help graphing this or choosing the correct graph? Let me know!

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Here are some related questions to explore:

1. What happens when you add a number **outside** the square root (e.g., \(f(x) = \sqrt{x} + 4\))?
2. How does the graph of \(g(x) = -\sqrt{x}\) differ from \(g(x) = \sqrt{x}\)?
3. What are the domain and range of \(f(x) = \sqrt{x + 4}\)?
4. How would you reflect the graph of \(f(x) = \sqrt{x + 4}\) across the \(x\)-axis?
5. How would the transformation change if the function were \(f(x) = \sqrt{-x + 4}\)?

**Tip:** Shifts to the left or right are always determined by the **opposite sign** of the number inside the function.

Describe how the graph of the function f(x) = √(x + 4) can be obtained from the basic graph g(x) = √x, then graph the function.

Explore how to transform the graph of the square root function g(x) = √x to obtain f(x) = √(x + 4). Learn how adding 4 inside the square root shifts the graph horizontally to the left by 4 units, with clear explanations and examples.

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