Find the domain and range of the relation, and state whether or not the relation is a function.
{(3, 9), (3, 10), (3, 11), (3, 12)}
the domain is the set of first elements, the range is the set of second elements, so the domain is
{3} and the range is {9,10,11,12}
Find the domain and range of the relation, and state whether or not the relation is a function.
{(3, 9), (3, 10), (3, 11), (3, 12)}
To find the domain and range of a relation, we need to consider the set of all input values (x-values) and the set of all output values (y-values) in the given relation.
In this relation, we see that each input value (3 in this case) corresponds to multiple output values, namely 9, 10, 11, and 12.
So, the domain of this relation is the set of all input values, which in this case is {3}.
The range of this relation is the set of all output values, which in this case is {9, 10, 11, 12}.
Now, to determine whether or not the relation is a function, we need to check if each input value (x-value) has a unique corresponding output value (y-value).
Since the input value 3 corresponds to multiple output values (9, 10, 11, and 12), this means that there are duplicate x-values, violating the definition of a function.
Therefore, the given relation is not a function.