To determine the domain of the function $f(x) = -x^2 - 8x - 12$, we need to consider if there are any restrictions on the variable $x$ (such as division by zero, square roots of negative numbers, etc.).

For a polynomial function like this one, which is a quadratic function, there are no such restrictions. The domain of a polynomial is always all real numbers because you can plug any real value of $x$ into the function without any issues.

Thus, the domain of the function is:

$\boxed{(-\infty, \infty)}$

Would you like to explore more about how this function behaves, or need any further clarification?

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Here are five related questions for you:

1. What is the range of the function $f(x) = -x^2 - 8x - 12$?
2. How can we find the vertex of a quadratic function?
3. What are the x-intercepts (if any) of the function $f(x) = -x^2 - 8x - 12$?
4. How do you complete the square to rewrite a quadratic in vertex form?
5. What does the negative sign in front of the $x^2$ term tell us about the shape of the graph?

Tip: For any quadratic function, the domain is always all real numbers, but the range depends on whether the parabola opens upwards or downwards.