A data analyst at a marketing firm is tracking the growth of a client's social media account over its first five months. The relationship between the month number and the total followers (in thousands) is recorded as the following relation: {(1, 1), (2, 8), (3, 27), (4, 64), (5, 125)}. Based on this data, which set represents the domain of the relation?

A data center technician monitors the power consumption of a server rack as more processors are activated. The relationship between the number of active processors ($x$) and the energy usage ($y$, in units) is recorded as the relation: E = {(1,1), (2,8), (3,27), (4,64), (5,125)}.

True or False: The range of this relation is the set {1, 2, 3, 4, 5}.

A logistics coordinator is calculating the storage capacities for five different cubic crates used in a warehouse. The relationship between the side length of each crate in meters ($x$) and its total volume in cubic meters ($y$) is recorded as the relation: R = {(1, 1), (2, 8), (3, 27), (4, 64), (5, 125)}. Match each mathematical description of this data set with its corresponding set or value.

Identifying Operational Parameters in Manufacturing

Inventory Management and Volume Scaling

An operations coordinator at a logistics warehouse tracks the total storage volume utilized across five designated storage zones. The relation between the zone number ($x$) and the space used in cubic meters ($y$) is logged as the set of ordered pairs: {(1, 1), (2, 8), (3, 27), (4, 64), (5, 125)}.

To find the range of this relation, the coordinator gathers the set of all unique second coordinates (the $y$-coordinates). When listed in ascending order, the range of this relation is {1, 8, 27, 64, ____}.

State the missing integer that completes this range.

An operations coordinator at a logistics warehouse is auditing the capacity records for five specialized cubic storage crates. The relationship between each crate's side length in meters ($x$) and its total volume in cubic meters ($y$) is logged as the relation: {(1,1), (2,8), (3,27), (4,64), (5,125)}. To present this data to the management team, the coordinator needs to formally extract and document the domain and range. Arrange the steps of this mathematical extraction in the correct chronological order.