Question

Determine the domain and the range of the​ relation, and tell whether the relation is a function.
​{(7​,10​), ​(29​,minus1​), ​(40​,10​), ​(7​,6​), ​(58​,6​)}

Answer 1

To determine the domain and range of the relation given by the set of ordered pairs \(\{(7, 10), (29, -1), (40, 10), (7, 6), (58, 6)\}\), we need to identify the unique values of the first elements (which make up the domain) and the unique values of the second elements (which make up the range).

### Domain
The domain consists of the first elements:
- From (7, 10), the first element is 7.
- From (29, -1), the first element is 29.
- From (40, 10), the first element is 40.
- From (7, 6), the first element is 7 (already counted).
- From (58, 6), the first element is 58.

So, the unique first elements (domain) are:
\[
\text{Domain} = \{7, 29, 40, 58\}
\]

### Range
The range consists of the second elements:
- From (7, 10), the second element is 10.
- From (29, -1), the second element is -1.
- From (40, 10), the second element is 10 (already counted).
- From (7, 6), the second element is 6.
- From (58, 6), the second element is 6 (already counted).

So, the unique second elements (range) are:
\[
\text{Range} = \{10, -1, 6\}
\]

### Is it a function?
A relation is a function if each element from the domain maps to exactly one element in the range. In this case, the element 7 from the domain maps to two different range values (10 and 6). Therefore, since there are multiple outputs for the input 7, this relation is **not a function**.

### Summary
- **Domain**: \(\{7, 29, 40, 58\}\)
- **Range**: \(\{10, -1, 6\}\)
- **Is it a function?**: No, it is not a function.