The given function is $f(x) = (x + 3)^2$.

To find the domain, we need to determine the set of all possible values of $x$ that make the function well-defined.

Analysis:

The expression $(x + 3)^2$ is a polynomial function. Polynomial functions are defined for all real values of $x$.

Domain:

The domain of $f(x) = (x + 3)^2$ is all real numbers: $\boxed{(-\infty, \infty)}$

Would you like a deeper explanation on how polynomials work in terms of domains or anything else?

Here are 5 related questions to explore:

1. What is the range of $(x + 3)^2$?
2. How does shifting a function horizontally affect its domain?
3. What is the domain of $\sqrt{(x + 3)^2}$?
4. How do you find the domain of rational functions?
5. What are the domain restrictions for trigonometric functions?

Tip: For most polynomial functions, their domain is all real numbers unless specified otherwise by other constraints (like square roots or denominators).