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Use the set of ordered pairs to determine whether the relation is a one-to-one function. {(−22,−15),(12,−1),(−22,6),(−10,13),(9,22),(20,−11)}

User Massquote
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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.

User Samu Lang
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