Which relation is a function? A. {(1, 2); (2, 3); (3, 4); (2, 5)} B. {(1, 2); (1, 3); (3, 2); (4, 2)} C. {(1, 2); (2, 3); (3, 4); (1, 5)} D. {(1, 2); (2, 5); (3, 2); (4, 5)} What is the range of the relation? {(1, 2), (2, 4), (3, 2),

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Alan P. Share
Apr 5, 2017

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See below for details.

Explanation:

When relations are defined by a set of paired values,
the first value in each pair is a Domain element
and the second value is a Range element.
We typically say that, for each pair the Domain element "maps into" the Range element.

A relation is a function if no Domain value "maps into" more than one Range value.

For the relations:
#A= {(1, 2); (2, 3); (3, 4); (2, 5)}#

the pairs #(2,3)# and #(2,5)# map the same Domain value (#2#) into different Domain values (#3# and #5#);
therefore #A# is not a function.

#B= {(1, 2); (1, 3); (3, 2); (4, 2)}#

the pairs #(1,2)# and #(1,3)# map the Domain value (#1#) into different Range values;
#B# is not a function.

#C: {(1, 2); (2, 3); (3, 4); (1, 5)}#

the pairs #(1,2)# and #(1,5)# map the Domain value (#1#) into different Range values;
#C# is not a function.

#D= {(1, 2); (2, 5); (3, 2); (4, 5)} #

there are no Domain values which map into more than one Range value;
#D# is a function.

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The Range of the relation #{(1, 2), (2, 4), (3, 2)}#
is the set of Range values, namely #{2,4}# (it is not necessary to include the value #2# in the Range set more than once).

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