Final answer:
The given relation is a function because each input maps to exactly one output, satisfying the definition of a function.
Step-by-step explanation:
To determine whether the given relation is a function, we need to check whether each input (x-value) maps to exactly one output (y-value). The relation consists of the pairs (−2, 1), (−4, −2), (3, 1), and (8, 9). By examining these ordered pairs, we note that there are no repeated x-values with different y-values, meaning each x-value is associated with only one y-value.
Therefore, based on the given definition, this relation is indeed a function because there is a one-to-one correspondence between x-values and y-values.
Professionally, understanding whether a set of data represents a function is crucial for analyzing the dependence of y on x and understanding the relationship between variables in various fields such as economics, science, and engineering.