If the domain of a relation is all whole numbers between 2.5 and​ 7.5, and the range contains 6 different​ values, can you determine whether the relation is a​ function? Explain your reasoning. Choose the correct answer below. A. The domain has more values than the​ range, so at least one range value is mapped to by more than one domain value. The relation is not a function. B. The domain has fewer values than the​ range, so there must be a domain value which maps to more than one range value. The relation is not a function. C. The domain has as many values as the​ range, but it cannot be determined whether the relation is a function with only the given information. D. The domain has as many values as the​ range, so each domain value maps to only one range value. The relation is a function.

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Answer:

This relation is not a function as the domain has fewer values than the​ range, so there must be a domain value which maps to more than one range value.

Step-by-step explanation:

A relation is said to be a function if each and every element of the domain has a distinct value value in the range.

Domain of a relation is a set of all whole numbers between 2.5 and​ 7.5, and the range contains 6 different​ values.

Whole numbers between 2.5 and 7.5 are [tex]3,4,5,6,7[/tex]

This relation is not a function as the domain has fewer values than the​ range, so there must be a domain value which maps to more than one range value.

B. This relation is not a function as the domain has fewer values than the​ range, so there must be a domain value which maps to more than one range value.

As we know that:

A relation is said to be a function if each and every element of the domain has a distinct value value in the range.

It is given that Domain of a relation is a set of all whole numbers between 2.5 and​ 7.5, and the range contains 6 different​ values.

Now, whole numbers between 2.5 and 7.5 are:

[tex]3,4,5,6[/tex]

There are 4 numbers in the domain and 6 numbers in the range.

That is the elements in domain are less than the elements in the range.

Therefore, this relation is not a function as the domain has fewer values than the​ range, so there must be a domain value which maps to more than one range value.

Hence the correct option is A.

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