For the following relation, give the domain and range, and indicate whether it is a function.
{(1,2),(6,3),(3,1),(8,7)}
To determine the domain and range and whether the given relation is a function, follow these steps:
1. Domain: The domain of a relation refers to the set of all possible input values (x-values). To find the domain, look at the x-values of each ordered pair in the relation. In this case, the domain would be {1, 6, 3, 8}, as these are the x-values present in the given pairs.
2. Range: The range of a relation refers to the set of all possible output values (y-values). To find the range, look at the y-values of each ordered pair in the relation. In this case, the range would be {2, 3, 1, 7}, as these are the y-values present in the given pairs.
3. Function: A relation is considered a function if each input value (x-value) from the domain corresponds to exactly one output value (y-value) from the range. To determine if the given relation is a function, check if there are any repeating x-values with different y-values. In this case, there are no repeating x-values, so each input value has a unique output value. Therefore, the given relation is a function.
In summary, for the given relation {(1,2),(6,3),(3,1),(8,7)}:
- Domain: {1, 6, 3, 8}
- Range: {2, 3, 1, 7}
- Function: Yes, it is a function.