Question

Find the domain and the range of the relation and determine whether it is a function.
​{(9​,4​),(minus2​,minus3​),(1​,minus2​),(5​,minus10​)}   
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Part 1
The domain is ​{
  
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Answer 1

To find the domain and range of the given relation and determine if it is a function, we analyze the provided set of ordered pairs: \((9, 4)\), \((-2, -3)\), \((1, -2)\), and \((5, -10)\).

### Part 1: Finding the Domain

The **domain** of a relation is the set of all first elements (x-coordinates) from each ordered pair.

From the given pairs, the x-coordinates are:
- 9
- -2
- 1
- 5

Thus, the domain is:
\[
\text{Domain} = \{9, -2, 1, 5\}
\]

### Part 2: Finding the Range

The **range** of a relation is the set of all second elements (y-coordinates) from each ordered pair.

From the given pairs, the y-coordinates are:
- 4
- -3
- -2
- -10

Thus, the range is:
\[
\text{Range} = \{4, -3, -2, -10\}
\]

### Part 3: Determining if it is a Function

A relation is considered a **function** if each input (x-coordinate) corresponds to exactly one output (y-coordinate).

In this case, all x-coordinates (9, -2, 1, and 5) are unique, meaning no x-coordinate is repeated. Therefore, each input corresponds to exactly one output.

Thus, this relation **is a function**.

### Summary

- **Domain**: \(\{9, -2, 1, 5\}\)
- **Range**: \(\{4, -3, -2, -10\}\)
- The relation **is a function**.