Question

what are the domain and range of this function?
(5, 10)
(4, 6)
(-7, -9)
(-3, 10)
(0, -4)
(7, -1)

domain: {-7, -3, 0, 5, 6, 7}
range: {-9, -4, -1, 6, 10}

domain: {-7, -3, 0, 4, 5, 7}
range: {-9, -4, -1, 6, 10}

domain: {-7, -3, 0, 4, 5, 7}
range: {-9, -4, -3, 6, 7, 10}

domain: {-7, -3, 0, 5, 6, 7}
range: {-9, -4, -3, 6, 7, 10}

Explanation:

Step1: Recall domain and range definitions

The domain of a function is the set of all input values (x - values from the ordered pairs), and the range is the set of all output values (y - values from the ordered pairs). The ordered pairs are \((5, 10)\), \((4, 6)\), \((-7, -9)\), \((-3, 10)\), \((0, -4)\), \((7, -1)\).

Step2: Find the domain

Extract the x - values from each ordered pair: \(5\), \(4\), \(-7\), \(-3\), \(0\), \(7\). So the domain is \(\{-7, -3, 0, 4, 5, 7\}\) (order does not matter in a set, but we list the unique x - values).

Step3: Find the range

Extract the y - values from each ordered pair: \(10\), \(6\), \(-9\), \(10\), \(-4\), \(-1\). After removing duplicates, the range is \(\{-9, -4, -1, 6, 10\}\) (again, order does not matter in a set).

Answer:

B. domain: \(\{-7, -3, 0, 4, 5, 7\}\)
range: \(\{-9, -4, -1, 6, 10\}\)