Question

suppose that the relation t is defined as follows. t = {(4, 5), (-6, 5), (-7, 0)} give the domain and range of t. write your answers using set notation. domain: range:

Explanation:

Step1: Find the domain

The domain of a relation is the set of all first elements (x - values) in the ordered pairs. For the relation \( T=\{(4, 5), (-6, 5), (-7, 0)\} \), the first elements are 4, -6, and -7.
So, the domain is the set containing these values: \( \{ -7, -6, 4 \} \) (we can order them for clarity, but set notation doesn't require a specific order).

Step2: Find the range

The range of a relation is the set of all second elements (y - values) in the ordered pairs. For the relation \( T=\{(4, 5), (-6, 5), (-7, 0)\} \), the second elements are 5, 5, and 0. Since a set does not contain duplicate elements, the range is the set containing 5 and 0: \( \{ 0, 5 \} \) (again, order in set notation is not fixed, but we can present it neatly).

Answer:

domain: \(\{ -7, -6, 4 \}\)
range: \(\{ 0, 5 \}\)