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The given function is \( h(x) = \sqrt{x + 5} \). To find the domain of this function, we need to determine the values of \( x \) that make the expression inside the square root non-negative because the square root function is only defined for non-negative numbers (i.e., the value inside the square root must be greater than or equal to zero).

### Step-by-step process:
1. Set the expression inside the square root to be non-negative:
   \[
   x + 5 \geq 0
   \]
2. Solve for \( x \):
   \[
   x \geq -5
   \]

### Domain:
Thus, the domain of the function \( h(x) \) is \( x \geq -5 \), or in interval notation:
\[
\text{Domain of } h(x): [-5, \infty)
\]

Would you like more details, or do you have any questions about this process?

Here are 5 questions related to this concept:
1. What is the range of the function \( h(x) = \sqrt{x + 5} \)?
2. How does the graph of \( h(x) = \sqrt{x + 5} \) look like compared to \( f(x) = \sqrt{x} \)?
3. What happens to the domain if the function was \( h(x) = \sqrt{-x + 5} \)?
4. How do you calculate the domain for a rational function?
5. What are the steps to find the domain when the function involves both square roots and fractions?

**Tip**: Always start by checking the inside of square roots or denominators when finding the domain of a function!

What is the domain of the function h(x) = √(x + 5)?

Learn how to determine the domain of the function h(x) = √(x + 5). Understand the key algebraic concepts and theorems related to square root functions. Suitable for students in Grades 9-10.

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