Question

Can a single ordered pair be a function?

Answer 1

i want to say no

Answer 2

That's what I thought but I wasn't sure because they question is worded as follows:

Consider the relation {(3,4)} which consists of a single ordered pair. Any set of one or more ordered pairs is a relation. Thus every function is a relation but not every relation is a function. Is this relation a function? What is its domain?

Answer 3

@phi

Answer 4

welll its arguable

Answer 5

Right but it's not a straight line it is just one ordered pair.

Answer 6

I can't tell....

Answer 7

well after googling, i guess you can consider it a function?

a constant function f(x) = c with a domain of a single point

Answer 8

http://answers.yahoo.com/question/index?qid=20090917080036AAaW9v6

Answer 9

Okay. Thanks. I appreciate your help. :)

Answer 10

sorry, i tried

Answer 11

I never thought about this, but I would say yes
The requirement for being a function is to be a "well-behaved" relation

Any set of one or more ordered pairs is a relation. So one ordered pair is a relation.

A well-behaved relation means
given an x, we get only and exactly one y

which is true for one ordered pair.

So the ordered pair (x0,y0) meets the criteria of being a well-behaved relation, which makes it a function, with domain of one value x0 and a range of one value, y0