The function given is:

$f(x) = |x - 2| - 8$

To find the domain of this function, we analyze the expression inside the function.

Step 1: Identifying Restrictions

The expression involves an absolute value, $|x - 2|$, and a constant $-8$. The absolute value function is defined for all real numbers, meaning that there are no restrictions on the values that $x$ can take.

Step 2: Domain of the Function

Since there are no restrictions, the domain of $f(x)$ includes all real numbers. In interval notation, the domain is:

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

If you want to confirm using graphing technology, you can graph $f(x) = |x - 2| - 8$ and observe that the graph is continuous for all $x$, without breaks or undefined points.

Let me know if you need further explanation on graphing this function!

Related Questions:

1. What is the range of the function $f(x) = |x - 2| - 8$?
2. How does shifting affect the graph of $f(x) = |x|$?
3. Can absolute value functions ever be undefined?
4. What does the graph of $f(x) = |x - 2| - 8$ look like?
5. How do transformations affect the shape of absolute value graphs?

Tip: Absolute value functions are always defined for all real numbers because they output non-negative values regardless of the input.