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The problem states:

Function \( g \) is defined by \( g(x) = \sqrt{x} \), and function \( f \) is defined by \( f(x) = \sqrt{x + 4} \). In the \( xy \)-plane, how does the graph of \( y = g(x) \) compare to the graph of \( y = f(x) \)?

To analyze this, we need to determine how the graph of \( f(x) = \sqrt{x + 4} \) relates to the graph of \( g(x) = \sqrt{x} \).

### Translation Analysis:
The graph of \( f(x) = \sqrt{x + 4} \) can be considered as a horizontal translation of the graph of \( g(x) = \sqrt{x} \). The expression \( \sqrt{x + 4} \) means that the graph of \( \sqrt{x} \) is shifted horizontally to the left by 4 units. 

**Conclusion:**
- The correct answer is option **D**: "The graph of \( y = f(x) \) is a translation of the graph of \( y = g(x) \) four units to the left."

Let me know if you would like further details or have any other questions! Here are 5 related questions you may find useful:

1. How do you determine if a graph is translated horizontally or vertically?
2. What happens to the graph of \( y = \sqrt{x} \) if we subtract a constant from \( x \)?
3. How would the graph change if the function was \( \sqrt{x - 4} \) instead of \( \sqrt{x + 4} \)?
4. Can translations be combined with other transformations like reflections or scaling?
5. How would the transformation differ for a function like \( y = x^2 \)?

**Tip:** Always remember that for horizontal translations, the shift is opposite to the sign inside the function: \( f(x - h) \) shifts to the right by \( h \) units, and \( f(x + h) \) shifts to the left by \( h \) units.

Function g is defined by g(x) = sqrt(x), and function f is defined by f(x) = sqrt(x + 4). In the xy-plane, how does the graph of y = g(x) compare to the graph of y = f(x)?

Explore how the graph of the square root function g(x) = sqrt(x) is horizontally translated by 4 units to the left to obtain the graph of f(x) = sqrt(x + 4). This concept is a fundamental part of graph transformations for high school algebra students.

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