State whether each of the following describes a function or not.

Question

a. Input: Name of a u.s. President. Output Date of birth of that president.

b. Input: Address of a house. Output: Name of a person who lives in the house.

c. Input: A positive integer. Output: Sum of the the digits of the integer. 

Answer 1

If you allow the number to be a mixed radix type. Such as that for time represented as weeks, days, hours. There is no unique way of representing this time for example 1 week and 1 day also means 8 days. The question almost surely means base 10 representation so that the sum of the digits is unique.

Answer 2

a:  Yes, because each president has only one birthday

 

b:  No, because there could be more than one person living in a house.  So there can be more than one output, which means it is not a function.

 

c:  It depends.  If you're only looking at base 10, then yes.  Each integer has only one way of being written in base 10, so you can only get one result from summing the digits.  But if you can include other bases, then no, because each base results in a different way of writing the integer, and the sum of the digits would generally be different for each one.  So there wouldn't be only one output in that case.