How do you know whether a relation is a function and what the domain and range is for #(1,-3), (6,-2), (9,-1), (1,3)#?

2 Answers
Mar 25, 2015

Answer:

This relation is not a function.
The domain of this relation is #{1, 6, 9}#
The range of this relation is #{-3, -2, -1, 3}#

Explanation:

A relation is a function if no two ordered pair in the relation have the same first element and different second elements.
(That is; If two different pair have the same first element then the relation is not a function.)

In #R={(1,-3), (6,-2), (9, -1), (1,3)}#

the pairs #(1, -3) # and #(1, 3)# cause this relation to not be a function.

The domain if the set of all first elements.
#"Domain"(R)={x| (EEy) [(x,y) in R}#

So the domain of your relation is #{1, 6, 9}#

The range is the set of second elements.
#"Range"(R)={y| (EEx) [(x,y) in R}#

So the range of your relation is #{-3, -2, -1, 3}#

Note
(Not all introductory level classes include domains and ranges for arbitrary relations. Some only mention domain and range for functions.)

Sep 17, 2017

Answer:

The given points DO NOT represent a function.

Domain# = {1,6,9}#

Range #={-3,-2,-1,3}#

Explanation:

A relation is a function if, for EACH #x# value there is only ONE possible #y# value.

As soon as there is a choice for #y#, it is not a function.

So #(3,1); (2,1); (1,1); (0,1)# IS a function because there is no choice for the #y# values.

It does not matter than several #x#-values all have the same #y#.

#(1,3);(1,4); (1,5); (1,6)# is NOT a function, because for the #x# value #x=1#, the #y# values can be #3 or 4 or 5 or 6#

In the given ordered pairs, if #x=1#, then #y=3 or -3#
This is therefore NOT a function.

The Domain is the set of all the #x#-values.
The Range is the set of all the #y# values.

For the given ordered pairs:

Domain# = {1,6,9}#

Range #={-3,-2,-1,3}#