To determine the domain and range of the relation [tex]\([(1, -8), (-7, 8), (-3, 7), (-3, -5)]\)[/tex], we need to follow these steps:
### Step 1: Identify the Domain
The domain consists of all the unique [tex]\(x\)[/tex]-values (the first elements) from each tuple in the relation. Let's extract them:
[tex]\[
(1, -8), (-7, 8), (-3, 7), (-3, -5)
\][/tex]
From these pairs, the [tex]\(x\)[/tex]-values are: [tex]\(1, -7, -3, -3\)[/tex].
### Step 2: Remove Duplicates in the Domain
To find the unique [tex]\(x\)[/tex]-values, we remove any duplicates:
[tex]\[
1, -7, -3
\][/tex]
Therefore, the domain is [tex]\([-3, -7, 1]\)[/tex].
### Step 3: Identify the Range
The range consists of all the unique [tex]\(y\)[/tex]-values (the second elements) from each tuple in the relation. Let's extract them:
[tex]\[
(1, -8), (-7, 8), (-3, 7), (-3, -5)
\][/tex]
From these pairs, the [tex]\(y\)[/tex]-values are: [tex]\(-8, 8, 7, -5\)[/tex].
### Step 4: Remove Duplicates in the Range
Since there are no duplicates in the [tex]\(y\)[/tex]-values, we simply list them as they are:
[tex]\[
-8, 8, 7, -5
\][/tex]
Therefore, the range is [tex]\([-8, 8, 7, -5]\)[/tex].
The correct answer is:
D. Domain [tex]\((-3, -7, 1)\)[/tex]; Range [tex]\((7, 8, -8, -5)\)[/tex]
