Write Relation as Ordered Pairs and Check Whether it is a Function
Question:
Write the following relation as sets of ordered pairs and determine whether it is a function:
$$
\{(x,y): y=3x,\ x\in\{1,2,3\},\ y\in\{3,6,9,12\}\}
$$
Solution
Given relation:
$$ y=3x $$
where
$$ x\in\{1,2,3\} $$
and
$$ y\in\{3,6,9,12\} $$
Find the value of \(y\) corresponding to each value of \(x\):
| \(x\) | \(y=3x\) |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
Therefore, the relation in roster form is:
$$ R=\{(1,3),(2,6),(3,9)\} $$
Checking Whether it is a Function
A relation is a function if every element of the domain has exactly one image.
Here:
- \(1\) has image \(3\)
- \(2\) has image \(6\)
- \(3\) has image \(9\)
Every element of the domain has exactly one corresponding value.
Therefore,
$$ \boxed{\text{The given relation is a function.}} $$