Final answer:
The domain of the function y = x^2 - 2x + 2 is all real numbers, expressed in set builder notation as x .
Step-by-step explanation:
The domain of a function refers to the set of all possible input values (x-values) that the function can accept without resulting in undefined or non-real values. When considering the function y = x^2 - 2x + 2, it is a quadratic function, and quadratics are defined for all real numbers. Therefore, the domain of this function in set builder's notation is x ∈ ℝ, where ℝ denotes the set of all real numbers.