https://file.aiquickdraw.com/mathbot/file/1725485204023ry7fs59o.jpg

To determine which equation represents the graph, let's analyze the provided options and compare them with the graph.

### Steps:
1. **Identify Key Features of the Graph:**
   - The graph starts at \( x = 2 \) with a \( y \)-value of 0.
   - The graph increases gradually, typical of a square root function.
   - The graph is shifted horizontally to the right, indicating a transformation.

2. **Analyze the Options:**
   - **Option 1:** \( f(x) = \sqrt{x + 2} \)
     - This function shifts the graph to the left by 2 units.
   - **Option 2:** \( f(x) = \sqrt{x} + 2 \)
     - This shifts the graph upwards by 2 units.
   - **Option 3:** \( f(x) = \sqrt{x - 2} \)
     - This shifts the graph to the right by 2 units.
   - **Option 4:** \( f(x) = \sqrt{x} - 2 \)
     - This shifts the graph downwards by 2 units.

### Conclusion:
The graph starts at \( x = 2 \) and the function that corresponds to this behavior is \( f(x) = \sqrt{x - 2} \), which shifts the basic square root function \( f(x) = \sqrt{x} \) to the right by 2 units.

So, **Option 3: \( f(x) = \sqrt{x - 2} \)** is the correct answer.

Would you like more details on this problem or have any questions?

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**Here are 5 related questions to expand your understanding:**
1. How do horizontal shifts affect the graph of a function?
2. How would the graph change if the function was \( f(x) = \sqrt{x - 4} \)?
3. What is the domain of the function \( f(x) = \sqrt{x - 2} \)?
4. How can you determine the range of a square root function?
5. What is the effect of a vertical shift on the graph of \( f(x) = \sqrt{x} \)?

**Tip:** For square root functions, the graph always starts at the point where the expression inside the square root becomes zero.

Which equation represents the graph? The graph shows a curve starting at (2, 0) and gradually increasing.

Determine the equation that represents a given graph with square root functions and horizontal shifts. This problem involves understanding function transformations, particularly horizontal shifts, suitable for Grades 9-11 students.

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