Question

what is the domain of this function?
(-3, -7)
(-8, 8)
(10, 1)
(9, 4)
(7, -4)
(-6, -9)
{-8, -6, 7, 9, 10} {1, 4, 7, 8, 9, 10}
{-8, -6, -3, 7, 9, 10} {-9, -7, -4, 1, 4, 8}

Explanation:

Step1: Recall domain definition

The domain of a function (given as ordered pairs) is the set of all first elements (x - values) of the ordered pairs.

Step2: Extract x - values

From the ordered pairs \((-3, -7)\), \((-8, 8)\), \((10, 1)\), \((9, 4)\), \((7, -4)\), \((-6, -9)\), the x - values (first elements) are \(-3\), \(-8\), \(10\), \(9\), \(7\), \(-6\).

Step3: Identify the set

Now we look for the set that contains these x - values: \(-8\), \(-6\), \(-3\), \(7\), \(9\), \(10\). This matches the set \(\{-8, -6, -3, 7, 9, 10\}\).

Answer:

\(\{-8, -6, -3, 7, 9, 10\}\) (the third option in the list of sets, which is \(\{-8, -6, -3, 7, 9, 10\}\))