https://file.aiquickdraw.com/mathbot/file/1727183002645f6ujglbo.jpg

Let's analyze the transformations from the given functions:

1. The original function is \( f(x) = \sqrt{x} \).
2. The transformed function is \( g(x) = 2\sqrt{x+4} - 7 \).

Now, let's break down the transformations:

- **Vertical Stretch**: The coefficient 2 in front of \( \sqrt{x+4} \) stretches the graph vertically. This is a **vertical stretch**.
- **Horizontal Shift**: The expression \( \sqrt{x+4} \) indicates a horizontal shift. Since it is \( x+4 \), the graph is shifted **4 units to the left**.
- **Vertical Shift**: The constant \(-7\) at the end subtracts 7 from the entire function, which shifts the graph **7 units down**.

### Conclusion:
The three transformations are:
1. Vertical Stretch
2. Horizontal Shift Left 4 units
3. Vertical Shift Down 7

Would you like a detailed explanation of any part of this transformation?

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Here are 5 questions to deepen your understanding:
1. How does changing the coefficient of the square root affect the graph of the function?
2. What would happen if the transformation was \( \sqrt{x-4} \) instead of \( \sqrt{x+4} \)?
3. How would the graph be different if the vertical shift was positive instead of negative?
4. What is the difference between a vertical stretch and a vertical compression?
5. How do you identify horizontal transformations based on the expression inside the square root?

**Tip**: Always remember that transformations inside the square root affect the graph horizontally, while transformations outside affect it vertically.

A function f(x) = √x is transformed into the function g(x) = 2√(x + 4) - 7. Choose the 3 transformations that occurred.

Analyze the transformation of the function f(x) = √x to g(x) = 2√(x + 4) - 7, including vertical stretch, horizontal shift, and vertical shift. This problem covers function transformation concepts and is suitable for students in Grades 9-11.

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