https://file.aiquickdraw.com/mathbot/file/1727065131663t5iv3ng1.jpg

The problem you're working on involves identifying the function \( g(x) \) based on the translation of \( f(x) = \sqrt{x} \).

The graph of \( f(x) = \sqrt{x} \) is shown in red, and the graph of \( g(x) \) is shown in green. To find \( g(x) \), we need to apply the translation rule between the red graph and the green graph.

Let's examine what type of transformation is applied to the red graph:

- Horizontal shifts: If the graph is shifted left or right, the transformation affects the \( x \)-coordinate inside the square root.
- Vertical shifts: If the graph is shifted up or down, the transformation affects the entire function by adding or subtracting a constant.

From the image, it appears that the green graph is a horizontal translation of the red graph. Specifically, it looks like the graph is shifted to the right by 4 units.

Thus, the transformation would be:
\[
g(x) = \sqrt{x - 4}
\]

This is because shifting \( f(x) = \sqrt{x} \) 4 units to the right results in \( g(x) = \sqrt{x - 4} \).

### Answer:
\[
g(x) = \sqrt{x - 4}
\]

Would you like more details on function transformations, or do you have any further questions?

Here are 5 related questions you might want to explore:
1. What happens to the graph of \( f(x) = \sqrt{x} \) if we shift it to the left by 2 units?
2. How would the graph change if we vertically translate \( f(x) = \sqrt{x} \) upwards by 3 units?
3. What is the effect of reflecting \( f(x) = \sqrt{x} \) across the x-axis on the equation of the function?
4. How does a vertical stretch affect the graph of \( f(x) = \sqrt{x} \)?
5. What would be the graph of \( g(x) = \sqrt{x + 6} \)?

**Tip:** Horizontal translations affect the input (inside the function), while vertical translations affect the output (outside the function).

The graph of f(x) = sqrt(x) is sketched in red and the graph of g(x) is sketched in green. Use the translation rule and f(x) = sqrt(x) to identify the function g(x).

Learn how to identify a translated square root function, g(x), using the translation rule. This problem involves horizontal translations of f(x) = sqrt(x), suitable for students in Grades 9-11.

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