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Given the relation:

[tex]\[ R = \{(-3, -2), (-3, 0), (-1, 2), (1, 2)\} \][/tex]

Select all numbers that are in the domain.

[tex]\[
\begin{array}{ll}
\checkmark & -3 \\
x & -2 \\
\checkmark & -1 \\
\times & 0 \\
\checkmark & 1 \\
x & 2 \\
\end{array}
\][/tex]

Select all numbers that are in the range.

[tex]\[
\begin{array}{ll}
x & -3 \\
\checkmark & -2 \\
\checkmark & 0 \\
\checkmark & 2 \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's go step by step to determine the domain and range of the relation [tex]\( R \)[/tex].

A relation [tex]\( R \)[/tex] is given by the set of ordered pairs:
[tex]\[ R = \{(-3, -2), (-3, 0), (-1, 2), (1, 2)\} \][/tex]

Step-by-Step Solution:

### Identifying the Domain:
The domain of a relation consists of all the first elements (x-coordinates) of the ordered pairs. Let's list them out:
1. From the pair [tex]\((-3, -2)\)[/tex], the first element is [tex]\(-3\)[/tex].
2. From the pair [tex]\((-3, 0)\)[/tex], the first element is [tex]\(-3\)[/tex].
3. From the pair [tex]\((-1, 2)\)[/tex], the first element is [tex]\(-1\)[/tex].
4. From the pair [tex]\((1, 2)\)[/tex], the first element is [tex]\(1\)[/tex].

Now, let's list the unique values among these:
[tex]\[ \{-3, -3, -1, 1\} \][/tex]

Remove the duplicate [tex]\(-3\)[/tex]:
[tex]\[ \{-3, -1, 1\} \][/tex]

So, the domain is [tex]\(\{-3, -1, 1\}\)[/tex].

### Identifying the Range:
The range of a relation consists of all the second elements (y-coordinates) of the ordered pairs. Let's list them out:
1. From the pair [tex]\((-3, -2)\)[/tex], the second element is [tex]\(-2\)[/tex].
2. From the pair [tex]\((-3, 0)\)[/tex], the second element is [tex]\(0\)[/tex].
3. From the pair [tex]\((-1, 2)\)[/tex], the second element is [tex]\(2\)[/tex].
4. From the pair [tex]\((1, 2)\)[/tex], the second element is [tex]\(2\)[/tex].

Now, let's list the unique values among these:
[tex]\[ \{-2, 0, 2, 2\} \][/tex]

Remove the duplicate [tex]\(2\)[/tex]:
[tex]\[ \{-2, 0, 2\} \][/tex]

So, the range is [tex]\(\{-2, 0, 2\}\)[/tex].

### Answering the Specific Questions:

#### Domain Selections:
- [tex]\(\checkmark \quad -3\)[/tex] (yes, it is in the domain)
- [tex]\(x \quad -2\)[/tex] (no, it is not in the domain)
- [tex]\(\checkmark \quad -1\)[/tex] (yes, it is in the domain)
- [tex]\(\times \quad 0\)[/tex] (no, it is not in the domain)
- [tex]\(\checkmark \quad 1\)[/tex] (yes, it is in the domain)
- [tex]\(x \quad 2\)[/tex] (no, it is not in the domain)

#### Range Selections:
- [tex]\(\times \quad -3\)[/tex] (no, it is not in the range)
- [tex]\(\checkmark \quad -2\)[/tex] (yes, it is in the range)
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