To determine which pairing describes a function, we need to ensure that for each unique input, there is exactly one associated output.
Let's analyze each pairing:
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(a person’s age in years, that same person’s height in inches): A person's height may change as they age during childhood but generally remains fixed for adults. However, if we consider individuals of the same age, they can have different heights. Therefore, this pairing does not describe a function.
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(a person’s weight in pounds, that same person’s height in inches): Similar to age and height, individuals with the same weight can differ in height. Thus, this pairing does not describe a function.
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(a person’s height in centimeters, that same person’s height in inches): The height converted from centimeters to inches is a direct and consistent mathematical relationship, meaning for each height in centimeters, there is exactly one corresponding height in inches. This pairing describes a function.
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(a person’s telephone number, that same person’s height in inches): A person's telephone number is unique, but multiple people can potentially have the same height. Therefore, this does not describe a function.
Based on this analysis, the pairing that always describes a function is: (a person’s height in centimeters, that same person’s height in inches).