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
Alan P.
Jun 30, 2016

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)).

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