Question

Identify the domain and range of the relation R={(10,6),(23,−1),(38,6),(10,4),(59,4)}. Determine if the relation represents a function.

Domain:

a) {10,23,38,59}

b) {6,−1,4}

c) {10,23,38,59,6,−1,4}

d) {6,4}

Answer 1

The domain of the relation is {10,23,38,59}, and the range is {6,−1,4}. However, the relation is not a function because the input '10' corresponds to two different outputs.

Step-by-step explanation:

To identify the domain and range of the relation R={(10,6),(23,−1),(38,6),(10,4),(59,4)}, we must look at the first and second elements of each ordered pair, respectively. The domain of a relation consists of all the first elements from the ordered pairs, while the range consists of all the second elements.

For the given relation R:

1. The domain is {10,23,38,59} because these are the unique first elements from each ordered pair.
2. The range is {6,−1,4} as these are the unique second elements.

Therefore, the correct choices are:

• Domain: a) {10,23,38,59}
• Range: b) {6,−1,4}

To determine if the relation represents a function, we need to check if each input (domain value) corresponds to exactly one output (range value). In this case, the input '10' corresponds to two different outputs ('6' and '4'), which means that the relation R is not a function.