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The question asks for the range of the function \( f(x) = x^2 \).

### Solution:

The function \( f(x) = x^2 \) is a **quadratic function** and is a parabola that opens upwards. 

1. **Domain**: The domain of \( f(x) = x^2 \) is all real numbers (\( x \in \mathbb{R} \)) because you can plug any real number into \( x^2 \).
   
2. **Range**: The range of \( f(x) = x^2 \) consists of all the possible output values. Since squaring any real number results in a non-negative number, the output (range) will always be \( y \geq 0 \). 

   - The smallest value of \( f(x) \) occurs at \( x = 0 \), where \( f(0) = 0^2 = 0 \).
   - As \( x \) moves away from 0 in either the positive or negative direction, \( f(x) \) increases.

Therefore, the **range** of the function \( f(x) = x^2 \) is all real numbers greater than or equal to 0, which is:

\[
\boxed{[0, \infty)}
\]

### Correct Answer:
Looking at the provided multiple-choice options, the correct answer is:
- \( \textbf{D) f(x) \geq 0} \)

If you have any questions or need further explanation, feel free to ask!

### Related Questions:
1. What is the domain of the function \( f(x) = x^2 \)?
2. How does the graph of \( y = x^2 \) compare to the graph of \( y = -x^2 \)?
3. How do you find the vertex of a parabola in general form?
4. What is the effect of adding a constant to the function \( f(x) = x^2 \)?
5. How would the range change for the function \( g(x) = (x-3)^2 + 1 \)?

### Tip:
When analyzing the range of a function, consider the possible output values that the function can produce based on its mathematical expression and any restrictions it might have.

What is the range of the function f(x) = x^2?

Learn how to find the range of the quadratic function f(x) = x^2. This solution explains the concept of a quadratic function, including the range of all real numbers greater than or equal to 0. Ideal for high school students in grades 9-12.

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