https://file.aiquickdraw.com/mathbot/file/172977333981242jydto6.jpg

The graph shown in the image is incorrect for the function \( f(x) = \sqrt{x} \). The function \( \sqrt{x} \) is only defined for \( x \geq 0 \), and its graph has the following properties:

1. The graph starts at the point \( (0, 0) \) because \( \sqrt{0} = 0 \).
2. It increases slowly to the right, forming a curve that is only in the first quadrant.
3. The curve never goes below the x-axis and does not exist in the negative x-values.

In the image, the graph appears to be a parabola, which is the wrong shape. A parabola typically represents quadratic functions such as \( f(x) = x^2 \), but not \( f(x) = \sqrt{x} \).

If you were looking for the correct graph of \( f(x) = \sqrt{x} \), it would:
- Start at the origin and curve upward, only extending into the first quadrant.

Do you want further details or have any other questions about this graph?

Here are 5 follow-up questions:
1. How do you graph the function \( f(x) = \sqrt{x} \) step by step?
2. What are the domain and range of the function \( f(x) = \sqrt{x} \)?
3. How does \( f(x) = \sqrt{x} \) differ from quadratic functions like \( f(x) = x^2 \)?
4. Can negative values be part of the input for \( f(x) = \sqrt{x} \)? Why or why not?
5. What transformations can be applied to the square root function to change its graph?

**Tip**: When graphing radical functions, always check the domain, as they might not be defined for certain values of \(x\).

Explore how to graph the square root function f(x) = √x, focusing on its domain, range, and properties. Understand why it is only defined for non-negative values and how it differs from quadratic functions like f(x) = x^2.

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