You are auditing a newly implemented HR database that links employee ID numbers ($x$-values) to their assigned department codes ($y$-values) using ordered pairs. During the audit, you review the following data set: {(105, 12), (108, 14), (105, 16), (110, 12)}. Recalling the definition of mathematical functions, what is the specific reason this set of ordered pairs does NOT represent a function?

A manufacturing supervisor records part data in a quality control log where the Part ID is the input ($x$) and the weight in grams is the output ($y$). The log contains the ordered pairs {}(702, 45.3) and {}(702, 45.8). True or False: This relation represents a mathematical function.

Auditing a Human Resources Database

As a Quality Control Auditor for a manufacturing database, you are verifying if the Part IDs ($x$) and their measured Tolerance Deviations ($y$) represent a mathematical function. Use your recall of function definitions to match the following terms with the correct descriptions based on this specific audit log: {(9, -3), (4, -2), (1, -1), (0, 0), (1, 1), (4, 2), (9, 3)}.

A financial analyst is reviewing a set of price changes ($y$) relative to a baseline index ($x$), recorded as the set of ordered pairs: {(9, -3), (4, -2), (1, -1), (0, 0), (1, 1), (4, 2), (9, 3)}. According to the definition of a mathematical function, this data set is not a function because the index value 9 is associated with two different price changes (-3 and 3), and the index value 4 is associated with both -2 and ____.

As an administrative assistant auditing a shipping company's database, you are creating a standard operating procedure (SOP) to check for data entry errors. You need to verify if the tracking records—which map Package ID ($x$-coordinates) to Weight ($y$-coordinates)—represent a mathematical function. Arrange the steps of the verification process in the correct logical order to recall and apply the definition of a function to identify a non-function relation.

Quality Control Calibration Audit