Questions: Determine if the relation is a function. Determine the domain and range for each. a) (3,4),(4,-6),(5,-7),(19,4),(-2,5) b) (-3,4),(-2,5),(0,0),(-2,11),(4,8)

Solution Steps

To determine if a relation is a function, we need to check if each input (first element of the pairs) maps to exactly one output (second element of the pairs). The domain is the set of all inputs, and the range is the set of all outputs.

For relation \( a = \{(3, 4), (4, -6), (5, -7), (19, 4), (-2, 5)\} \), each input maps to exactly one output. Thus, relation \( a \) is a function.

The domain of relation \( a \) is the set of all first elements: \[ \text{Domain}(a) = \{3, 4, 5, 19, -2\} \] The range of relation \( a \) is the set of all second elements: \[ \text{Range}(a) = \{-7, -6, 4, 5\} \]

For relation \( b = \{(-3, 4), (-2, 5), (0, 0), (-2, 11), (4, 8)\} \), the input \(-2\) maps to two different outputs (5 and 11). Therefore, relation \( b \) is not a function.

The domain of relation \( b \) is: \[ \text{Domain}(b) = \{0, 4, -3, -2\} \] The range of relation \( b \) is: \[ \text{Range}(b) = \{0, 4, 5, 8, 11\} \]

Final Answer