To determine the domain and range of the given relation [tex]\( G \)[/tex], we will follow these steps:
1. Identify the elements of the relation [tex]\( G \)[/tex]:
[tex]\[
G = \{(3,-2), (-4,-4), (-2,0), (-9,5)\}
\][/tex]
2. Extract the domain:
The domain of a relation is the set of all first elements (x-coordinates) of the ordered pairs. From the given relation [tex]\( G \)[/tex], we can list the first elements:
- For the pair [tex]\( (3, -2) \)[/tex], the first element is [tex]\( 3 \)[/tex].
- For the pair [tex]\( (-4, -4) \)[/tex], the first element is [tex]\( -4 \)[/tex].
- For the pair [tex]\( (-2, 0) \)[/tex], the first element is [tex]\( -2 \)[/tex].
- For the pair [tex]\( (-9, 5) \)[/tex], the first element is [tex]\( -9 \)[/tex].
Therefore, the domain is the set of all these first elements. In set notation, this is:
[tex]\[
\text{Domain} = \{ 3, -4, -2, -9 \}
\][/tex]
3. Extract the range:
The range of a relation is the set of all second elements (y-coordinates) of the ordered pairs. From the given relation [tex]\( G \)[/tex], we can list the second elements:
- For the pair [tex]\( (3, -2) \)[/tex], the second element is [tex]\( -2 \)[/tex].
- For the pair [tex]\( (-4, -4) \)[/tex], the second element is [tex]\( -4 \)[/tex].
- For the pair [tex]\( (-2, 0) \)[/tex], the second element is [tex]\( 0 \)[/tex].
- For the pair [tex]\( (-9, 5) \)[/tex], the second element is [tex]\( 5 \)[/tex].
Therefore, the range is the set of all these second elements. In set notation, this is:
[tex]\[
\text{Range} = \{ 0, -4, 5, -2 \}
\][/tex]
Hence, the domain and range of the relation [tex]\( G \)[/tex] are:
[tex]\[
\text{Domain} = \{ 3, -4, -2, -9 \}
\][/tex]
[tex]\[
\text{Range} = \{ 0, -4, 5, -2 \}
\][/tex]
