The relation is a function because each input value corresponds to one output value.
In Mathematics and Geometry, a function defines and represents the relationship that exists between two or more variables in a relation, table, ordered pair, or graph.
Generally speaking, a function uniquely maps all of the input values (domain) to the output values (range).
By critically observing each of the table of values, we can reasonably infer and logically deduce that this table of values represents a function because each of the input values are uniquely mapped to one output value only.