https://file.aiquickdraw.com/mathbot/file/1726974790528vrvjbq26.jpg

The function given is \( y = \sqrt{x - 4} \). This is a square root function that is shifted horizontally.

### Steps to analyze the graph:

1. **Basic Form**: The base square root function is \( y = \sqrt{x} \). The graph starts at the origin \((0,0)\) and increases gradually, only defined for non-negative \(x\).

2. **Shift of the Graph**: 
   - The expression inside the square root, \( x - 4 \), represents a horizontal shift. Specifically, it shifts the graph **4 units to the right**. So instead of starting at \( x = 0 \), the graph now starts at \( x = 4 \).
   - There is no vertical shift, as there is no term added or subtracted outside of the square root function.

3. **Domain**: The square root function is only defined for \( x \geq 4 \) (since the expression inside the square root must be non-negative).

4. **Range**: Since the square root outputs only non-negative values, the range of the function is \( y \geq 0 \).

### Identifying the correct graph:

The graph should start at the point \( (4, 0) \) and increase gradually to the right.

- In the image, Graph B shows the point starting at \( (4, 0) \) and then increases to the right, which matches the expected graph of \( y = \sqrt{x - 4} \).

### Answer:
The correct graph is **B**.

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Would you like a more detailed breakdown of the steps or more examples?

Here are five related questions for you to consider:
1. How does the graph of \( y = \sqrt{x + 4} \) differ from \( y = \sqrt{x - 4} \)?
2. What would happen to the graph if there was a vertical shift, such as \( y = \sqrt{x - 4} + 2 \)?
3. What is the domain and range of the function \( y = -\sqrt{x - 4} \)?
4. How do you find the inverse of the function \( y = \sqrt{x - 4} \)?
5. How would the graph change if the function was \( y = \sqrt{2x - 8} \)?

### Tip:
When graphing square root functions, always pay attention to shifts inside the square root (horizontal) and outside the square root (vertical).

Explore how to graph the square root function y = sqrt(x - 4) by applying horizontal shifts. Learn step-by-step to identify the correct graph, understand domain and range, and visualize function transformations. Ideal for students in Grades 9-11.

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