Question

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)}?

Answer 1

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)`).