Questions: Suppose that the relation (H) is defined as follows. (H=(7,-2),(-3,-8),(0,7),(-3,9)) Give the domain and range of (H). Write your answers using set notation. ( text domain =) range =

Solution Steps

The domain of a relation is the set of all first elements (x-coordinates) from each ordered pair. For the relation \( H = \{(7,-2),(-3,-8),(0,7),(-3,9)\} \), we extract the x-coordinates:

• From \((7, -2)\), the x-coordinate is \(7\).
• From \((-3, -8)\), the x-coordinate is \(-3\).
• From \((0, 7)\), the x-coordinate is \(0\).
• From \((-3, 9)\), the x-coordinate is \(-3\).

The domain is the set of these x-coordinates, without repetition. Therefore, the domain is \(\{7, -3, 0\}\).

The range of a relation is the set of all second elements (y-coordinates) from each ordered pair. For the relation \( H = \{(7,-2),(-3,-8),(0,7),(-3,9)\} \), we extract the y-coordinates:

• From \((7, -2)\), the y-coordinate is \(-2\).
• From \((-3, -8)\), the y-coordinate is \(-8\).
• From \((0, 7)\), the y-coordinate is \(7\).
• From \((-3, 9)\), the y-coordinate is \(9\).

The range is the set of these y-coordinates, without repetition. Therefore, the range is \(\{-2, -8, 7, 9\}\).

Final Answer