Question

which relation is not a function? {((1,-5), (-1,6), (1,5), (6,-3))} {((2,7), (3,7), (4,7), (5,8))} {((1,-5), (3,1), (-5,4), (4,-2))} {((3,-2), (5,-6), (7,7), (8,8))}

Explanation:

Step1: Recall function definition

A relation is a function if each input (x - value) has exactly one output (y - value). So we check each relation for repeated x - values with different y - values.

Step2: Analyze first relation

First relation: \(\{(1, - 5),(-1,6),(1,5),(6,-3)\}\)
Here, the x - value \(1\) is paired with \(y=-5\) and \(y = 5\). Since one input (\(x = 1\)) has two different outputs, this relation is not a function.

Step3: Verify other relations (optional for identification)

• Second relation: \(\{(2,7),(3,7),(4,7),(5,8)\}\)

All x - values (\(2\), \(3\), \(4\), \(5\)) are unique or have the same y - value (for \(2\), \(3\), \(4\)), so it is a function.

• Third relation: \(\{(1,-5),(3,1),(-5,4),(4,-2)\}\)

All x - values (\(1\), \(3\), \(-5\), \(4\)) are unique, so it is a function.

• Fourth relation: \(\{(3,-2),(5,-6),(7,7),(8,8)\}\)

All x - values (\(3\), \(5\), \(7\), \(8\)) are unique, so it is a function.

Answer:

\(\{(1, - 5),(-1,6),(1,5),(6,-3)\}\) (the first relation in the list)