How do you find the domain and the range of the relation, and state whether or not the relation is a function {(1, 3), (2, 3), (3, 3), (4, 3)}?

1 Answer
Jun 30, 2016

Answer:

The given set is a function
with a domain of #{1,2,3,4}#
and a range of #{3}#

Explanation:

A set #{(1,3),(2,3),(3,3),(4,3)}#
can be considered to be a relation #color(red)(x)rarrcolor(blue)(y)#
with #(color(red)(x),color(blue)(y))in{(color(red)(1),color(blue)(3)),(color(red)(2),color(blue)(3)),(color(red)(3),color(blue)(3)),(color(red)(4),color(blue)(3))}#

The domain is the collection of values associated with #color(red)(x)# within this relationship, namely #{color(red)(1,2,3,4)}#

The range is the collection of values associated with #color(blue)(y)# within this relationship, namely#{color(blue)(3)}#

The relationship is a function if no values of #color(red)(x)# are each associated with more than one value of #color(blue)(y)#. (Note that the inverse is not necessarily true; a single value of #color(blue)(y)# may have more than one corresponding value of #color(red)(x)#).