Which of the following relation are functions? Give reasons. In cane of a function, determine its domain and range.
`{(1,-2),(3,7),(4,-6),(8,11)}`

Answer

To determine whether the given relation is a function, we need to analyze the set of ordered pairs:

\[ \{(1, -2), (3, 7), (4, -6), (8, 11)\} \]

### Step 1: Check if the relation is a function
A relation is a function if every input (first element of each ordered pair) is associated with exactly one output (second element of each ordered pair).

- The first elements of the ordered pairs are: 1, 3, 4, and 8.
- None of these first elements are repeated.

Since all first elements are unique, we can conclude that this relation is indeed a function.

### Step 2: Determine the domain
The domain of a function is the set of all first elements from the ordered pairs.

- From the pairs, the first elements are: 1, 3, 4, and 8.

Thus, the domain is:
\[ \text{Domain} = \{1, 3, 4, 8\} \]

### Step 3: Determine the range
The range of a function is the set of all second elements from the ordered pairs.

- From the pairs, the second elements are: -2, 7, -6, and 11.

Thus, the range is:
\[ \text{Range} = \{-2, 7, -6, 11\} \]

### Conclusion
The given relation is a function. The domain is \(\{1, 3, 4, 8\}\) and the range is \(\{-2, 7, -6, 11\}\).

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