Final answer:
The relation given by the set of ordered pairs is not a one-to-one function because the x-value −22 is associated with two different y-values, which violates the definition of a one-to-one function.
Step-by-step explanation:
Is the Relation a One-to-One Function?
To determine whether a relation is a one-to-one function, each input (x-value) in the set of ordered pairs must be mapped to exactly one unique output (y-value). A function is considered one-to-one if no input corresponds to more than one output.
Let's analyze the given set of ordered pairs: {(−22,−15), (12,−1), (−22,6), (−10,13), (9,22), (20,−11)}. For this set to represent a one-to-one function, each x-value can only appear once since each must map to a different y-value.
Upon inspection, the x-value −22 appears twice, once paired with −15 and once with 6. This means the relation assigns two different outputs (−15 and 6) to the same input (−22), which violates the definition of a one-to-one function.
Therefore, the relation given by the provided set of ordered pairs is not a one-to-one function.