A data processing system uses an identity function to ensure that a numerical input is transmitted to the next stage without any modification. Which equation and set of properties correctly define this function?

In industrial automation, a 'Pass-Through' data sensor is programmed using the identity function to ensure that every numerical value it receives is recorded exactly as it is without any modification. As a technician reviewing the system's documentation, match each mathematical property of this sensor's behavior with its correct value or expression.

A technician calibrating a high-precision digital scale uses the identity function $f(x) = x$ to ensure that the weight displayed on the screen is exactly equal to the weight of the object on the scale. True or False: The graph of this function is a straight line that passes through the origin $(0, 0)$ and has a slope of ${}1$.

Geometric Properties of the Identity Function

A technician calibrating a digital scale uses the equation $f(x) = x$ to ensure that the weight shown on the display is always exactly equal to the weight of the object on the scale. This specific mathematical relationship is formally known as the ____ function.