Question

Consider the two groups listed below. Which statement correctly describes the relationship of the two sets if they were mapped?

all eighth grade students
birthdays

A The relation (students, birthdays) is a function, but the relation (birthdays, students) is not.
B The relation (birthdays, students) is a function, but the relation (students, birthdays) is not.
C Both relations (students, birthdays) and (birthdays, students) are functions.
D Neither the relation (students, birthdays) nor the relation (birthdays, students) is a function

Answer 1

(students, birthdays) is a function because it is a many to one or one to one relation . ( 1 student cant have 2 birthdays).

(birthdays , students ) is not a function because more than one student may have the same birthday ( this is a one to many relation)

Its A

Answer 2

A The relation (students, birthdays) is a function, but the relation (birthdays, students) is not.

Explanation:

A function is a relation in which each input value, or x-coordinate, is mapped to one output, or y-coordinate. No x-coordinate can be used more than once.

The relation (students, birthdays) has students as the x-value and birthdays as the y-value. In order for this to be a function, each student would have to have only one birthday. This is true; no student has more than one birthday. This is a function.

The relation (birthdays, students) has birthdays as the x-value and students as the y-value. In order for this to be a function, each birthday would have to have only one student associated with it. This is not true; each birthday can have multiple people celebrating that day. This is not a function.