Question

which relation is a function?
a. {(8, 2), (8, 5), (8, 0), (8, -4)}

b. {(2, 2), (4, 5), (-4, 5), (6, 7)}

c. {(0, 2), (2, 5), (4, 6), (4, 7)}

d. {(-4, -6), (-3, -5), (2, -4), (2, -3)}

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze Option A

In the set \(\{(8,2),(8,5),(8,0),(8, - 4)\}\), the x - value \(8\) is paired with multiple y - values (\(2\), \(5\), \(0\), \(-4\)). So this is not a function.

Step3: Analyze Option B

In the set \(\{(2,2),(4,5),(-4,5),(6,7)\}\), each x - value (\(2\), \(4\), \(-4\), \(6\)) is paired with exactly one y - value. The x - value \(4\) and \(-4\) both pair with \(5\), but that is allowed (multiple inputs can have the same output, just not the same input with multiple outputs).

Step4: Analyze Option C

In the set \(\{(0,2),(2,5),(4,6),(4,7)\}\), the x - value \(4\) is paired with two different y - values (\(6\) and \(7\)). So this is not a function.

Step5: Analyze Option D

In the set \(\{(-4,-6),(-3,-5),(2,-4),(2,-3)\}\), the x - value \(2\) is paired with two different y - values (\(-4\) and \(-3\)). So this is not a function.

Answer:

B. \(\{(2,2),(4,5),(-4,5),(6,7)\}\)