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Example: Determining Whether Ordered Pairs Represent a One-to-One Function
Consider two sets of ordered pairs to determine if each is a function and, if so, whether it is one-to-one.
ⓐ The set : Each -value is paired with only one -value, so the relation is a function. However, examining the -values reveals repetitions — for instance, the pairs and share the same -value of , and the pairs and share the -value of . Because not every -value corresponds to a unique -value, this function is not one-to-one.
ⓑ The set : Each -value maps to exactly one -value, confirming it is a function. Additionally, each -value — , , , , and — appears only once, meaning every -value is paired with a unique -value. Therefore, this function is one-to-one.
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Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
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Example: Determining Whether Ordered Pairs Represent a One-to-One Function
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