A distribution center tracks the deviation of a package's weight from its target ($x$) and the corresponding cost adjustment ($y$). The data is recorded as the set: $\{(-4, 8), (-2, 4), (-1, 2), (0, 0), (1, 2), (2, 4), (4, 8)\}$. Based on the definition of a one-to-one function, why is this relation NOT considered one-to-one?

A machine calibration log records a setting adjustment ($x$) and the corresponding error output ($y$) as the set of ordered pairs: $\{(-4, 8), (-2, 4), (-1, 2), (0, 0), (1, 2), (2, 4), (4, 8)\}$. This relation is considered a one-to-one function because no $x$-value is repeated in the pairings.

A warehouse inventory system tracks the deviation from a target stock level ($x$) and the resulting priority level ($y$). The data is recorded as the set: $\{(-4, 8), (-2, 4), (-1, 2), (0, 0), (1, 2), (2, 4), (4, 8)\}$. Match each priority level ($y$) with the pair of deviation values ($x$) that result in that same priority, demonstrating why the relation is not a one-to-one function.

Identifying Repeated Outputs in Logistics Data

A warehouse management system assigns a priority level ($y$) to inventory locations based on their distance from the main loading dock ($x$). The mapping is represented by the following set of ordered pairs: $\{(-4, 8), (-2, 4), (-1, 2), (0, 0), (1, 2), (2, 4), (4, 8)\}$. According to the definition of a one-to-one function, this relation is NOT one-to-one because the priority level of ____ is assigned to both the location at $x = -4$ and the location at $x = 4$.

Function Types in Machine Calibration Data