Question

what is the range of this relation?
(2, 2)
(1, 4)
(-3, 5)
(7, 2)
(6, 9)
(7, -5)
{-5, 2, 4, 5, 9} {-5, 1, 2, 5, 9}
{-3, 2, 5, 6, 9} {-3, 1, 2, 6, 7}

Explanation:

Step1: Recall the definition of range

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

Step2: Identify the y - values from each ordered pair

• For the ordered pair \((2,2)\), the y - value is \(2\).
• For the ordered pair \((1,4)\), the y - value is \(4\).
• For the ordered pair \((- 3,5)\), the y - value is \(5\).
• For the ordered pair \((7,2)\), the y - value is \(2\) (we already have \(2\) in our set, but we still list it once in the set).
• For the ordered pair \((6,9)\), the y - value is \(9\).
• For the ordered pair \((7,-5)\), the y - value is \(-5\).

Step3: List the unique y - values

The unique y - values are \(-5,2,4,5,9\). We then order them (though the order in a set does not matter, we can check against the options) and we get the set \(\{-5,2,4,5,9\}\).

Answer:

\(\{-5, 2, 4, 5, 9\}\)