which relation represents a function?

Question

a )the students in your class(domain),with the year of their birth date(range)
b)The color of each car sold by a car dealership in a month(domain) with the names of the people who bought it(range)
c)the types of cofee sold at a cofee shop(domain) with the names of the people that buy each type(range)
d the number of legs on each animal in a zoo(domain) with the name of the animal (range)

Explanation too please thank you

Answer 1

In order for a relation to be a function, it must assign one, and only one, value to each element of it's domain. So,

a) It's a function, because to each student there corresponds one and only one year of his/her birth date.

b) Not a function, because to each color there can correspond several names. Sevela people with different names can but cars of the same color

c) Not a function, same reason that in (b)

d) Not a function, because to a same number of legs there corresponds several different animals.

Answer 2

It's the first one, because a function has a unique element of the range for each element of the domain. Theres a unique birthday(range) for each student in your class(domain).

The rest are not functions because for example, in (b), two people(range) can buy a car of the same color (domain). This applies to (c) also. In (d), many animals (range) can have the same number of legs(domain).

All this means is that if I give you a person, you can certainly tell me their birthday(or find out). If I am talking about a four legged animal, however, you have no way of knowing whether it is a lion or a lizard.