Question

Find the domain and the range of the relation and determine whether it is a function.
​{(9​,1​),(minus7​,minus4​),(1​,minus1​),(3​,minus8​)}   

Answer 1

To determine the domain and range of the given relation \(\{(9, 1), (-7, -4), (1, -1), (3, -8)\}\) and to check whether it is a function, follow these steps:

1. **Domain**: The domain of a relation is the set of all first elements (x-values) in the ordered pairs.

From the given relation, the first elements (x-values) are:
- 9
- -7
- 1
- 3

Therefore, the domain is:
\[
\text{Domain} = \{9, -7, 1, 3\}
\]

2. **Range**: The range of a relation is the set of all second elements (y-values) in the ordered pairs.

From the given relation, the second elements (y-values) are:
- 1
- -4
- -1
- -8

Therefore, the range is:
\[
\text{Range} = \{1, -4, -1, -8\}
\]

3. **Function Check**: A relation is considered a function if each input (x-value) is associated with exactly one output (y-value). In this case, we check the x-values to see if there are any repeats.

The x-values are:
- 9
- -7
- 1
- 3

Since all x-values are unique and no x-value is repeated with a different y-value, the relation is indeed a function.

In summary:
- **Domain**: \(\{9, -7, 1, 3\}\)
- **Range**: \(\{1, -4, -1, -8\}\)
- **Is it a function?**: Yes.