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.

A logistics coordinator is analyzing delivery routes using a tracking system. The system records the relative distance from a central hub in miles (represented as the input $x$) and the corresponding fuel consumption rate in gallons (represented as the output $y$). The coordinator collects the following dataset of coordinates:

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

To determine how to program the route optimization software, the coordinator must recall the correct classification of this dataset. Since every unique input $x$-value is paired with exactly one output $y$-value, this relation is mathematically classified as a ____.

Thermal Sensor Performance Analysis