To find the domain of the function $f(x) = \sqrt{x+4}$, we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not defined in the set of real numbers.

The expression inside the square root is $x + 4$. For $f(x)$ to be defined, we require:

$x + 4 \geq 0$

Solving this inequality:

$x \geq -4$

Thus, the domain of the function $f(x) = \sqrt{x+4}$ is:

$\boxed{[-4, \infty)}$

This means that the function is defined for all $x$ such that $x \geq -4$.

Would you like more details or have any questions?

Here are 5 questions related to this topic:

1. How would the domain change if the function were $\sqrt{x-2}$?
2. What is the range of the function $f(x) = \sqrt{x+4}$?
3. How would the graph of $f(x) = \sqrt{x+4}$ look?
4. What happens to the domain if we square the function?
5. How do we find the domain of a function with both a square root and a fraction?

Tip: Always check for restrictions like square roots and fractions to determine the domain of a function.