Determine the domain and range of the following relations : `{(-3,1),(-1,1),(1,0),(3,0)}`

Answer

To determine the domain and range of the given relation, we will follow these steps:

### Step 1: Identify the Ordered Pairs
The given relation consists of the following ordered pairs:
\[ \{(-3,1), (-1,1), (1,0), (3,0)\} \]

### Step 2: Determine the Domain
The domain of a relation is the set of all first elements (x-coordinates) from the ordered pairs.

- From the first pair \((-3, 1)\), the first element is \(-3\).
- From the second pair \((-1, 1)\), the first element is \(-1\).
- From the third pair \((1, 0)\), the first element is \(1\).
- From the fourth pair \((3, 0)\), the first element is \(3\).

Now we collect all unique first elements:
\[ \text{Domain} = \{-3, -1, 1, 3\} \]

### Step 3: Determine the Range
The range of a relation is the set of all second elements (y-coordinates) from the ordered pairs.

- From the first pair \((-3, 1)\), the second element is \(1\).
- From the second pair \((-1, 1)\), the second element is \(1\) (already counted).
- From the third pair \((1, 0)\), the second element is \(0\).
- From the fourth pair \((3, 0)\), the second element is \(0\) (already counted).

Now we collect all unique second elements:
\[ \text{Range} = \{1, 0\} \]

### Final Result
Thus, the domain and range of the given relation are:
- **Domain**: \(\{-3, -1, 1, 3\}\)
- **Range**: \(\{1, 0\}\)

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