Question

State the domain and range of each relation. Then graph the relation and determine whether it is a function.

65. $\left\{\left(0,2\right),\left(1,3\right),\left(2,-1\right),\left(1,0\right)\right\}$

Short answer

The domain of the given relation is $\left\{0,1,2\right\}$and range is $\left\{2,3,-1,0\right\}$.

Step-by-step solution

Step 1- Given information

A relation set$\left\{\left(0,2\right),\left(1,3\right),\left(2,-1\right),\left(1,0\right)\right\}$.

Step 2- Concept used

The domain of a relation set is the set of all first elements of the ordered pairs.

The range of a relation set is the set of all second elements of the ordered pairs.

A relation set is called a function if every element of domain has a unique image.

Step 3- To find domain and range

The relation set is:

$\left\{\left(0,2\right),\left(1,3\right),\left(2,-1\right),\left(1,0\right)\right\}$

The domain of the given relation set is:

$\left\{0,1,2\right\}$

The range of the given relation set is:

$\left\{2,3,-1,0\right\}$

Here, each element of the domain has not a unique image.

As 1 have two image 3 and 0.

So, the given relation set is not a function.

Step 4- The graph of the relation

The graph of the given relation is: