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.