https://file.aiquickdraw.com/mathbot/file/1730398848037iapgeg6r.jpg

To solve this, let’s analyze the function provided:

The function is:
\[
y = \sqrt{x + 4}
\]
with the restriction \( x \geq -4 \).

### Step 1: Determine the Domain of \( y = \sqrt{x + 4} \)
For the square root function to be defined, the expression inside the square root must be non-negative:
\[
x + 4 \geq 0 \Rightarrow x \geq -4
\]
Thus, the domain of this function is \( x \geq -4 \).

### Step 2: Determine the Range of \( y = \sqrt{x + 4} \)
For \( y = \sqrt{x + 4} \):
- The minimum value of \( x \) is \(-4\), which makes \( y = \sqrt{-4 + 4} = \sqrt{0} = 0 \).
- As \( x \) increases, \( y = \sqrt{x + 4} \) also increases without bound.

Therefore, the range of \( y = \sqrt{x + 4} \) is:
\[
y \geq 0
\]

### Step 3: Select the Correct Answer
Looking at the provided answer choices in the dropdown menu, the correct range for this function is:
\[
y \geq 0
\]

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

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Here are some related questions for further practice:
1. What is the inverse of \( y = \sqrt{x + 4} \)?
2. How does the range of a square root function generally behave?
3. What happens to the domain and range if the function changes to \( y = \sqrt{x - 4} \)?
4. How would the range change if the function had a restriction \( y \leq 4 \)?
5. Can we define a function with \( y = \sqrt{x + 4} \) over all real numbers?

**Tip:** For functions involving square roots, remember that the expression inside the square root must be non-negative to keep values in the real number domain.

The range of the function y = √(x + 4), x ≥ -4, is ____. For each input of the given domain of y = √(x + 4), there ____. For this reason, the inverse of y = √(x + 4), x ≥ -4, is ____.

Understand how to determine the range of the function y = √(x + 4) with the domain restriction x ≥ -4. This problem explores the concepts of square root functions, domain, and range, suitable for high school students in Grades 9-11.

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