Final answer:
The function f(x) = (x-1)² - 4 is not one-to-one because it produces multiple outputs for different inputs.
Step-by-step explanation:
The function f(x) = (x-1)² - 4 is not one-to-one because it fails the horizontal line test. A one-to-one function is a function where each input has a unique output. However, in this case, for every x value, there are two different y values.
For example, let's consider x = 0 and x = 2. When x = 0, f(x) = (-1)² - 4 = 3. When x = 2, f(x) = (1)² - 4 = -3. Therefore, the function is not one-to-one because it produces multiple outputs for different inputs.