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The problem in the image is asking you to graph the function \( h(x) = \sqrt{x - 2} \) by applying transformations to the base function \( f(x) = \sqrt{x} \). It also asks to find the domain and range of the function.

### Step-by-Step Solution:

1. **Base Function**: The basic function is \( f(x) = \sqrt{x} \). The graph of this function starts at \( (0,0) \) and increases to the right, being defined only for \( x \geq 0 \).

2. **Transformation**: The function \( h(x) = \sqrt{x - 2} \) represents a **horizontal shift** of the base function \( \sqrt{x} \) to the right by 2 units. The transformation here is \( x - 2 \), which shifts the graph 2 units to the right.

   - **Shift**: Every point on the graph of \( \sqrt{x} \) moves right by 2 units.

3. **Domain**: Since the square root function \( \sqrt{x - 2} \) is only defined when \( x - 2 \geq 0 \), we solve:
   \[
   x - 2 \geq 0 \quad \Rightarrow \quad x \geq 2
   \]
   So, the domain is \( [2, \infty) \).

4. **Range**: The square root function always produces non-negative values. So the range remains \( [0, \infty) \).

### Correct Graph:
The graph of \( h(x) = \sqrt{x - 2} \) starts at \( (2, 0) \) and rises to the right. This matches **Option D** from the multiple-choice options shown in the image.

Would you like more details or have any other questions?

### Related Questions:
1. What happens to the graph of \( \sqrt{x} \) if you replace \( x \) with \( x + 3 \)?
2. How does a vertical stretch affect the graph of \( f(x) = \sqrt{x} \)?
3. How do you find the domain of a general square root function \( \sqrt{g(x)} \)?
4. What is the effect of a vertical shift on a square root function?
5. How do you reflect the graph of a square root function across the x-axis?

**Tip**: For transformations, always remember that changes inside the function (with \( x \)) affect the graph horizontally, while changes outside affect it vertically.

Graph the function h(x) = sqrt(x - 2) by using the techniques of shifting, compressing, stretching, and reflecting. Find the domain and range of the function.

Learn how to graph the transformed function h(x) = sqrt(x - 2) by applying horizontal shifts. This problem covers the domain and range of the function, suitable for students in Grades 9-11.

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