Question

what is the range of this relation?
(8, 4)
(7, 9)
(4, -3)
(3, -1)
{3, 4, 7, 8} {-3, 1, 4, 8}
{-3, -1, 4, 9} {-1, 3, 4, 9}

Explanation:

Step1: Recall the definition of range

The range of a relation (set of ordered pairs) is the set of all the second elements (y - values) of the ordered pairs.

Step2: Identify the second elements

For the ordered pairs \((8, 4)\), \((7, 9)\), \((4, - 3)\), \((3, - 1)\), the second elements (y - values) are \(4\), \(9\), \(-3\), and \(-1\).

Step3: Form the set of range values

We collect these y - values and form a set. The set of these values is \(\{-3, - 1, 4, 9\}\).

Answer:

\(\{-3, - 1, 4, 9\}\) (corresponding to the option \(\{-3, - 1, 4, 9\}\) among the given choices)