Which statement below is correct for the following set of ordered pairs?

{(0, 1.2), (3, 2), (−1.2, 3), (4, −2), (1, −1.2), (1.2, 4)}

a the set is a function since each element in the domain has a different element in the range.

b the set is a function since each element in the range has a different element in the domain.

c the set is not a function since each element in the domain has a different element in the range.

d the set is not a function since each element in the range has a different element in the domain.

We observe the set doesn't have two points with the same x value, so this is a function.  Let's look at the answers.

a The set is a function since each element in the domain has a different element in the range.

No, this is more the idea of one-to-one or injectivity.

b The set is a function since each element in the range has a different element in the domain.

This isn't quite right either but we're going to choose it as the best answer.  It's not that each element in the range has a different element in the domain; that would be onto aka surjectivity.  It's that each element in the set, each point, has a different element in the domain, a different y coordinate.  It's ok if two different x coordinates map to the same y coordinate, which they don't here but they could.

b

c The set is not a function since each element in the domain has a different element in the range.

Nope, it is a function.

d The set is not a function since each element in the range has a different element in the domain.

Nope, it is a function.

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