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)}
In a function, for any x you give me, I can find one and only one value of y
looks like if x=3, y = 9 but also y = 10, and 11 and 12
You decide! Is it a function?
To find the domain and range of a relation, we need to examine the set of inputs (x-values) and outputs (y-values) in the relation.
Let's consider the given relation: {(3,9), (3,10), (3,11), (3,12)}.
Domain:
The domain of a relation consists of all the unique x-values in the ordered pairs. In this case, every ordered pair has an x-value of 3. Since there are no other x-values present, the domain is simply {3}.
Range:
The range of a relation consists of all the unique y-values in the ordered pairs. Looking at the given relation, the y-values are 9, 10, 11, and 12. Therefore, the range is {9, 10, 11, 12}.
Functionality:
To determine if the relation is a function, we need to verify that each x-value in the domain has only one corresponding y-value in the range. In the given relation, the x-value 3 has four corresponding y-values (9, 10, 11, and 12). Since an x-value should have only one corresponding y-value in a function, this relation is not a function.
In summary:
Domain: {3}
Range: {9, 10, 11, 12}
Functionality: Not a function