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Identify the root function represented by the following graph write in Square Root Function with Vertical Translation: 

The graph you uploaded shows a curve that looks like a modified version of a square root function. The basic form of a square root function is:

\[
y = \sqrt{x}
\]

However, the graph suggests that the function has been translated both vertically and horizontally. It starts rising from approximately \(x = 1\), which indicates a horizontal translation to the right, and it is also shifted slightly upward.

The general form of a square root function with vertical and horizontal translations is:

\[
y = a \sqrt{x - h} + k
\]

Where:
- \(a\) controls the vertical stretch or compression,
- \(h\) controls the horizontal translation (shift),
- \(k\) controls the vertical translation.

Looking at the graph:
- The graph starts to rise at around \(x = 1\), suggesting \(h = 1\) (a horizontal shift to the right by 1).
- The function seems to be slightly translated upward, so \(k\) appears to be positive, possibly \(k = 1\).

Therefore, the equation of the function could be something like:

\[
y = \sqrt{x - 1} + 1
\]

This would correspond to a square root function that is translated 1 unit to the right and 1 unit up.

Would you like more details or have any questions?

### Related Questions:
1. What does the parameter \(a\) in the function \(y = a\sqrt{x-h} + k\) affect?
2. How can you determine the horizontal shift from a graph?
3. What effect does \(k\) have on the graph of a square root function?
4. How would the graph change if \(a\) were negative?
5. How do vertical stretches or compressions change the shape of the square root graph?

**Tip:** To determine translations, always observe where the graph starts and how far it has been shifted from the origin.

Identify the root function represented by the following graph write in Square Root Function with Vertical Translation.

Learn how to identify a square root function with horizontal and vertical translations from a graph. This example involves translating the function y = √(x - h) + k, showing how the curve shifts horizontally by 1 unit and vertically by 1 unit. Suitable for high school students in Grades 10-12.

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