https://file.aiquickdraw.com/mathbot/file/172610574926998i7lv6v.jpg

The function given in the image is:

\[
y = \sqrt{x + 2}
\]

Let's find the domain and range of this function.

**Domain:**
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the square root function, the expression inside the square root must be non-negative, because the square root of a negative number is not real.

So, we set up the inequality:

\[
x + 2 \geq 0
\]

Solving this inequality:

\[
x \geq -2
\]

Therefore, the domain of the function is:

\[
\text{Domain} = [-2, \infty)
\]

**Range:**
The range of a function is the set of all possible output values (y-values). For \(y = \sqrt{x + 2}\), since the square root function outputs non-negative values (i.e., \(y \geq 0\)), we can determine the range as follows:

- When \(x = -2\), \(y = \sqrt{-2 + 2} = 0\).
- As \(x\) increases, \(y\) also increases because the square root function is increasing.

Thus, the range of the function is:

\[
\text{Range} = [0, \infty)
\]

So, the domain is \([-2, \infty)\) and the range is \([0, \infty)\).

Would you like further details, or do you have any questions?

Here are some related questions you might find helpful:

1. How do you find the domain and range of a function with multiple restrictions?
2. What happens to the domain and range if the function is \(y = \sqrt{-x + 2}\)?
3. How can we graph the function \(y = \sqrt{x + 2}\)?
4. What are the domain and range of the function \(y = \sqrt{x - 2}\)?
5. How do the transformations of a square root function affect its domain and range?

**Tip:** Always check inside the square root for domain restrictions and remember that the square root function only outputs non-negative values unless otherwise modified.

Find the domain and range of y = √(x + 2).

Learn how to find the domain and range of the square root function y = √(x + 2). This step-by-step solution includes detailed explanations about the conditions for the domain and range, perfect for students in Grades 9-11.

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