Question

Let A denote the set of all people who were alive in 2010. Let B denote the set of all real numbers. Let f assign, to each person in A, their weight during the year 2010. Is f a function? Explain in complete sentences.

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Birdie

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Yes, (f) is a function. In mathematical terms, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. In this case, the set (A) (the set of all people who were alive in 2010) is the domain, and the set (B) (the set of all real numbers) is the codomain. The function (f) assigns to each person in (A) their weight during the year 2010. Since each person in (A) has exactly one weight, each element in (A) is associated with exactly one element in (B). Therefore, (f) is a function. It’s important to note that the weights (outputs) can be the same for different people (inputs), but each person (input) has exactly one weight (output). This is consistent with the definition of a function.

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