What is the domain of the function y = StartRoot x EndRoot + 4?
Negative infinity less-than x less-than infinity
Negative 4 less-than-or-equal-to x less-than infinity
0 less-than-or-equal-to x less-than infinity
4 less-than-or-equal-to x less-than infinity

To determine the domain of the function \( y = \sqrt{x} + 4 \), we need to identify the values of \( x \) for which the function is defined. 

The function involves a square root, which is only defined for non-negative values of \( x \). This is because the square root of a negative number is not a real number. Therefore, \( x \) must be greater than or equal to 0. There is no upper limit to the values that \( x \) can take.

So, the domain of the function \( y = \sqrt{x} + 4 \) is:
\[ 0 \leq x < \infty \]

Thus, the correct answer is:
\[ \boxed{0 \leq x < \infty} \]

Would you like more details or have any questions about this solution?

Here are some related questions for further exploration:
1. What is the range of the function \( y = \sqrt{x} + 4 \)?
2. How would the domain change if the function were \( y = \sqrt{x-4} + 4 \)?
3. What is the domain of the function \( y = \sqrt{4 - x} \)?
4. How does the addition of a constant outside the square root affect the domain of the function?
5. What is the domain of the function \( y = \sqrt{x^2 - 4} \)?

**Tip:** When dealing with square root functions, always consider the values of \( x \) that make the expression inside the square root non-negative.

What is the domain of the function y = √x + 4?

Understand how to find the domain of the function y = √x + 4. Explore key mathematical concepts such as square root functions and domain restrictions. The function y = √x + 4 is defined for x ≥ 0, providing a thorough breakdown suitable for students in Grades 9-11.

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