Question

In: Math

A certain business keeps a database of information about its customers. A. Let C be the...

A certain business keeps a database of information about its customers. A. Let C be the rule which assigns to each customer shown in the table his or her home phone number. Is C a function? Explain your reasoning.

Expert Solution

If we assume that every person has

(i) a home phone number

(ii) no more than one home phone number

then and only then rule is a function.

Let us denote the people by , where stands for the first name in the book, for the second name, etc. Let the corresponding phone numbers be denoted by , where is the phone number of , is the phone number of and so on.

If for any and if , i.e. the phone numbers of and are different then and are two different people because one person is assumed not to have more than one home phone number.

So, .

Thus, we have for any . Taking the contrapositive we get for any . So is a function.

But if any person, say is allowed to have more than one phone numbers, then the value of is not unique. Therefore does not become a function in such a case.

Also if some person does not have a home phone number, then does not exist, and therefore does not become a function in such a case.

P.S.: Please upvote if you have found this answer helpful.

milcah answered 2 years ago

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