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.