Question

State whether the following mapping represents a function. Then give the domain and range.

Answer 1

Answer:

Please check the explanation.

Step-by-step 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}