Answer:
Please check the explanation.
Explanation:
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
Let us create the table from the given mapping
x y
2 20
2 40
4 40
3 30
From the table, it is clear that the input x = 2 is repeated twice. In other words, the input x = 2 is duplicated.
- i.e. at x = 2, y = 20 and at x = 2, y = 40
As we know that we can not have duplicated inputs as there should be only 1 output for each input.
Therefore, the given relation/mapping DOES NOT represent a function.
Determining the domain of a relation:
We know that the domain of the relation is the set of all the x-coordinates of the given points or ordered pairs.
Thus, the domain of the relation in ascending order is:
Domain D = {2, 3, 4}
- Please note the duplicated elements in the domain or range of a relation are written only once.
Determining the range of a relation:
We know that the range of the relation is the set of all the y-coordinates of the given points or ordered pairs.
Thus, the range of the relation in ascending order is:
Domain D = {20, 30, 40}