https://file.aiquickdraw.com/mathbot/file/1730161164397j8lz5ett.jpg

To solve this, let's analyze the problem:

1. The parent function given is \( f(x) = \sqrt{x} \), shown by the dashed blue curve in the graph.
2. The function \( h(x) \) is a transformation of \( f(x) \), resulting in the solid black curve in the graph.

### Observing the Transformation:
From the graph, we can see that \( h(x) \) is shifted vertically upward compared to \( f(x) \). This indicates a vertical transformation.

1. A vertical shift of a function \( f(x) = \sqrt{x} \) by a constant \( k \) is represented as \( h(x) = \sqrt{x} + k \).
2. Looking at the graph, it appears that \( h(x) \) is shifted 4 units upward from \( f(x) \).

### Conclusion:
The correct function for \( h(x) \) should be:
\[
h(x) = \sqrt{x} + 4
\]

### Answer:
The correct option is:
- **A. \( h(x) = \sqrt{x} + 4 \)**

Would you like more details or have any further questions?

### Related Questions:
1. How does a horizontal shift affect the square root function?
2. What happens if we apply both horizontal and vertical shifts to \( \sqrt{x} \)?
3. How would the graph change if we reflected \( f(x) = \sqrt{x} \) over the x-axis?
4. What transformation would result in \( h(x) = \sqrt{x - 4} \)?
5. How does multiplying \( f(x) = \sqrt{x} \) by a constant affect the graph?

### Tip:
Vertical shifts in functions involve adding or subtracting a constant directly to the function (outside the square root), while horizontal shifts affect the input inside the square root.

The function h(x) is a transformation of the square root parent function, f(x) = √x. What function is h(x)?

Identify the transformation of the square root function f(x) = √x to determine the function h(x). This problem explores vertical shifts and transformations of functions, suitable for students in Grades 9-10.

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