Question

Suppose that the relation S is defined as follows. S= {(4,9), (-9,4), (0, -9), (6, 6)} Give the domain and range of S. Write your answers using set notation.

domain =
range = ​

Answer 1

Given:

The relation S is:

`S=\{(4,9),(-9,4),(0,-9),(6,6)\}`

To find:

The domain and range of S.

Solution:

If a relation is defined by the set of ordered pairs (x,y), then the domain is the set of x-values and range is the set of y-values.

Let R be a relation defined as
`R=\{(x,y):x\in R,y\in R\}`, then
`Domain=\{x:x\in R\}` and
`Range=\{y:y\in R\}`.

The given relation is:

`S=\{(4,9),(-9,4),(0,-9),(6,6)\}`

Here, x-values are 4,-9,0,6 and the y-values are 9,4,-9,6.

So, the domain and range of the given relation S are

`Domain=\{-9,0,4,6\}`

`Range=\{-9,4,6,9\}`

Therefore,
`Domain=\{-9,0,4,6\}` and
`Range=\{-9,4,6,9\}`.