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The given graph depicts a transformation of the basic square root function \( y = \sqrt{x} \).

Let's break down the transformation:

1. **Horizontal Shift**: The graph appears to be shifted to the left, as the starting point (where \( y = 0 \)) seems to occur at \( x = -2 \). This indicates a horizontal shift by 2 units to the left, which suggests a transformation of \( \sqrt{x+2} \).

2. **Vertical Shift**: The graph's starting point (vertex) is also raised to \( y = 2 \), indicating a vertical shift 2 units up. This means we add 2 to the entire function.

3. **No Reflection or Stretching**: The shape of the graph suggests that there are no reflections (no negative signs) or vertical stretches/compressions applied.

Thus, the transformed function can be written as:

\[
y = \sqrt{x + 2} + 2
\]

Would you like more details, or do you have any questions?

Here are some related questions you might want to explore:

1. How do horizontal shifts affect the square root function?
2. What happens to the graph of \( y = \sqrt{x} \) if we apply a vertical reflection?
3. Can the transformation include both horizontal and vertical stretching or compressing?
4. How does a vertical shift affect the domain and range of the square root function?
5. What would the equation look like if there were a vertical stretch applied?

**Tip:** When analyzing graph transformations, always check for horizontal and vertical shifts, stretches/compressions, and reflections. Each of these affects the graph in predictable ways.

Write the expression for the transformation of the square root function shown below.

Explore the transformation of the square root function with horizontal and vertical shifts. The function moves left by 2 units and up by 2 units, resulting in the equation y = √(x + 2) + 2. Learn how to identify shifts in function graphs with this step-by-step explanation.

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