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Discuss why the function f(x) = (x-1)² - 4 is not one-to-one.

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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.

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