Q64. - Algebra 2

Question

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

64. $\left\{\left(-1,5\right),\left(1,3\right),\left(2,-4\right),\left(4,3\right)\right\}$

Step-by-Step Solution

Answer

The domain of the given relation is $\left\{-1,1,2,4\right\}$and range is $\left\{5,3,-4,3\right\}$.

Step 1- Given information

A relation set $\left\{\left(-1,5\right),\left(1,3\right),\left(2,-4\right),\left(4,3\right)\right\}$.

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:

$\left\{\left(-1,5\right),\left(1,3\right),\left(2,-4\right),\left(4,3\right)\right\}$

The domain of the given relation set is:

$\left\{-1,1,2,4\right\}$

The range of the given relation set is:

$\left\{5,3,-4,3\right\}$

Here, each element of the domain has a unique image.

So, the given relation set is a function.

Step 4- The graph of the relation