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The problem asks which graph corresponds to the equation \( y = 2\sqrt{x} + 2 \), and it provides a reference graph of \( y = \sqrt{x} \). To understand how the transformations work, let's break it down:

1. **Starting Function**: The graph of \( y = \sqrt{x} \) is already given. It is a basic square root function with the following properties:
   - It starts at the origin \((0, 0)\).
   - It increases slowly as \( x \) increases.

2. **Transformations in \( y = 2\sqrt{x} + 2 \)**:
   - **Vertical Stretch**: The term \( 2\sqrt{x} \) applies a vertical stretch by a factor of 2. This makes the graph grow twice as fast as \( y = \sqrt{x} \). In other words, for the same value of \( x \), the \( y \)-coordinate is doubled.
   - **Vertical Shift**: The \( +2 \) at the end shifts the entire graph upward by 2 units.

### Step-by-step:
- The original graph of \( y = \sqrt{x} \) starts at \( (0,0) \). 
- The transformation \( 2\sqrt{x} + 2 \) will now start at \( (0, 2) \), since the vertical shift moves the graph 2 units upward.
- The vertical stretch by 2 means that for any \( x \), the graph's height will be twice as high as the original.

### Expected Graph:
- It will start at \( (0, 2) \).
- It will have a similar shape to the graph of \( y = \sqrt{x} \), but it will rise more steeply due to the vertical stretch.

Would you like further clarification or a detailed graphing example?

Here are 5 questions to explore this concept more:
1. How does changing the coefficient in front of \( \sqrt{x} \) affect the graph?
2. What is the domain of the function \( y = 2\sqrt{x} + 2 \)?
3. How would the graph change if the transformation included a horizontal shift?
4. What is the range of the new function?
5. How would you describe the behavior of the function as \( x \) approaches infinity?

**Tip**: Always look at how each transformation (stretch, shift) affects the basic shape of the function.

Which of the following is the graph of y = 2√x + 2?

Learn how to graph the transformed square root function y = 2√x + 2. This problem demonstrates vertical stretch and vertical shift, helping students understand graph transformations. Suitable for Grades 8-10.

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