https://r2.erweima.ai/mathbot/image/17247201199548eyuf6jf.jpg

The image you provided shows a graph of the equation \( y = 2\sqrt{x} \). The graph appears to be correctly plotted on a coordinate plane, with the curve representing the function.

### Key Points of the Graph:
1. **Equation:** The equation \( y = 2\sqrt{x} \) is a transformation of the basic square root function \( y = \sqrt{x} \), scaled by a factor of 2.
2. **Domain:** Since square roots of negative numbers are not real, the domain of this function is \( x \geq 0 \).
3. **Range:** Since \( \sqrt{x} \) is non-negative and is multiplied by 2, the range of this function is \( y \geq 0 \).
4. **Shape:** The graph starts at the origin \((0, 0)\) and increases as \( x \) increases, forming a curve that opens to the right.
5. **Transformation:** The multiplication by 2 causes the graph to stretch vertically, making it steeper compared to \( y = \sqrt{x} \).

Would you like more details or have any questions about this function or its graph?

### Related Questions:
1. What is the effect of multiplying a square root function by a constant?
2. How would the graph change if the equation were \( y = \sqrt{x} + 3 \)?
3. What are the domain and range of the function \( y = -2\sqrt{x} \)?
4. How does the square root function compare to quadratic functions in terms of graph shape?
5. What happens to the graph if you apply a horizontal shift, such as \( y = 2\sqrt{x - 1} \)?

### Tip:
When graphing square root functions, always consider the domain first, as the function is not defined for negative values of \( x \) in the real number system.

Explore the graph of the function y = 2√x, including its domain, range, shape, and vertical transformation. This detailed analysis covers essential concepts in square root functions and their graphical representations. Suitable for students in Grades 10-12.

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