Final answer:
The domain of the quadratic function y = x² - 2x - 1 is all real numbers, and the range is all real numbers greater than or equal to -2.
Step-by-step explanation:
The domain and range of a function describe the set of possible input values (domain) and output values (range). For the quadratic function y = x² - 2x - 1, the domain is all real numbers since a quadratic function is defined for every real value of x.
The range of a quadratic function in the form of y = ax² + bx + c where a > 0 is all real numbers greater than or equal to the vertex's y-value. The vertex form of the given function can be found by completing the square, which leads us to y = (x-1)² - 2. The vertex is at (1, -2), thus the range is y ≥ -2.
Therefore, the domain is all real numbers, which can be expressed as (-∞, ∞), and the range is all real numbers greater than or equal to -2, or [-2, ∞).