The given function is:

$f(x) = \frac{x + 2}{x - 8}$

The domain of a function is the set of all real numbers for which the function is defined. For a rational function like this, the function is undefined wherever the denominator equals zero.

The denominator of $f(x)$ is $x - 8$. Setting this equal to zero, we get:

$x - 8 = 0 \implies x = 8$

Thus, the function is undefined when $x = 8$. Therefore, the domain of $f(x)$ is all real numbers except $x = 8$.

Final Answer: The domain is all real numbers except $x = 8$.

Would you like further details or examples on this concept?

Here are 5 questions to expand your understanding:

1. How do you find the domain for a function with multiple factors in the denominator?
2. What happens to the graph of $f(x)$ at $x = 8$? (Hint: vertical asymptote)
3. How do the numerator's properties affect the domain of a rational function?
4. How do you find the domain for functions involving square roots or logarithms?
5. How can you verify the domain of a function graphically?

Tip: Always check both the numerator and denominator for restrictions, as they can both affect the domain of a rational function.