In a workplace database tracking project assignments, each 'Project ID' (input) is paired with a 'Budget Amount' (output). Which of the following conditions must be met for this relation to be considered a mathematical function?

An operations analyst is reviewing a performance log that relates 'Task Complexity' (the input) to 'Resource Units Used' (the output). The log is represented by the following set of ordered pairs:

$S = \{(-3, 27), (-2, 8), (-1, 1), (0, 0), (1, 1), (2, 8), (3, 27)\}$

Match each mathematical term with the corresponding data set or rule from the log.

A technician is monitoring a system that outputs data as a set of ordered pairs: $\{(-3, 27), (-2, 8), (-1, 1), (0, 0), (1, 1), (2, 8), (3, 27)\}$. This relation is correctly classified as a mathematical function because each unique input value is paired with exactly one output value.

Identifying Range in Professional Data Mapping

A logistics manager is reviewing a cost schedule where 'Zone ID' is the input and 'Handling Fee' is the output, represented by the set: $S = \{(-3, 27), (-2, 8), (-1, 1), (0, 0), (1, 1), (2, 8), (3, 27)\}$. To verify that this relation is a mathematical function, arrange the following analytical steps in the correct order.