Function? Correspondence? Neither?

[Kinetica]

Homework Statement

Consider the following mathematical items. For each item, (1) indicate whether it has a natural interpretation as a function, a correspondence, or neither. If the item is a function or a correspondence, the indicate (2) its domain and range and (3) whether it is (a) real, (b) single-valued and (c) univariate.
If the item is not a function, or is not real, single-valued or univariate, then justify your answer briefly.

The Attempt at a Solution

1. (1,1), (2,2), (3,3) is a function. Domain (1,2, 3), Range (1,2, 3) Single-valued?

2. (1,1), (2,2), (1,3) is NOT a fuction. Domain (1,2), Range (1,2, 3) Single-valued

3. (1,1), (2,1), (3,1) is a function. Domain (1,2, 3), Range (1) Single-valued

4. (1,1), (2,(3,1)), (3,1) is a function. Domain (1,2, 3), Range (1, 3)-is it correct? Univariate

5) ((1,1),2), ((2,1),3), ((2,1),4) is NOT a function. Domain (?), Range (2,3,4) Univariate

Any mistakes?

 

[Office_Shredder]

For number 4, what is f(2) supposed to be?

 

[Kinetica]

Our teacher jumped into the material and barely covered it. So I still don't understand what (2,(3,1)) means.

 

[Office_Shredder]

Ok. We are representing a function as a set of ordered pairs. The first entry is going to be x, and the second entry is going to be f(x).

So for number 1, f(1)=1 since (1, 1) is in the set, f(2)=2 since (2,2) is in the set, f(3)=3 since (3,3) is in the set.

For number 3, f(1)=1 since (1,1) is in the set; f(2)=1 since (2,1) is in the set and f(3)=1 since (3,1) is in the set

 

[Kinetica]

Oh, this part, I understand.
The one I am talking about (2,(3,1)) is correspondence, when one or more elements of domain are mapped to more than one element from the range. Typically, what is a range of this example?

I am also struggling with whether it is (a) real, (b) single-valued and (c) univariate.