Final answer:
The correct statement is that the domain of the function y = log(x - 2) + 1 is (2, ∞), and the range is all real numbers, as the logarithm can yield any real number and the +1 shifts the entire function vertically without restricting the output values.
Step-by-step explanation:
For the function y = log(x - 2) + 1, we need to consider the properties of the logarithm function to determine its domain and range. The logarithm function is defined only for positive arguments. Therefore, the domain of x - 2 must be positive, which means x must be greater than 2. This makes the domain of the function (2, ∞). Since the logarithm function can produce any real number as an output, the range of the function is all real numbers. However, since the whole function is increased by 1, the result of the logarithm will always be shifted up by 1 unit, yet will still cover all real numbers.