Let's analyze the function $y = f(x) = \log(x - 3)$.

Domain:

For the logarithmic function $\log(x - 3)$, the argument inside the logarithm, $x - 3$, must be greater than 0. This is because the logarithm of a non-positive number is undefined.

So, the condition for the domain is:

$x - 3 > 0 \quad \Rightarrow \quad x > 3$

Thus, the domain of the function is:

$\boxed{(3, \infty)}$

Range:

For the range of the logarithmic function, we know that the output of a logarithmic function can take any real value. This is because the logarithmic function maps positive inputs to all real numbers.

Thus, the range of the function is:

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

Conclusion:

The correct answer is:

b. Domain: (3, ∞); Range: (-∞, ∞)

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Would you like any further explanation or details? Here are 5 related questions to deepen your understanding:

1. What happens to the graph of $y = \log(x - 3)$ as $x$ approaches 3 from the right?
2. How would the domain and range change for a function like $y = \log(x + 3)$?
3. What is the behavior of the function $y = \log(x - 3)$ when $x \to \infty$?
4. Can the logarithmic function be defined for negative values or zero? Why or why not?
5. What would be the effect of multiplying $\log(x - 3)$ by a constant, such as $y = 2 \log(x - 3)$?

Tip: Always check the domain restrictions first when dealing with logarithmic and other special functions.