Question

which relation is not a function?
a {(1,2),(1,3),(1,4),(1,5)}
b {(-1,6),(0,7),(5,11),(12,22)}
c {(0,3),(6,7),(1,9),(4,16)}
d {(-1,3),(-5,10),(5,6),(1,-1)}

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). In other words, no two ordered pairs in the relation can have the same x - value with different y - values.

Step2: Analyze Option A

For the relation \(\{(1,2),(1,3),(1,4),(1,5)\}\), the x - value \(x = 1\) is paired with multiple y - values (\(y=2\), \(y = 3\), \(y=4\), \(y = 5\)). So, this relation does not satisfy the definition of a function.

Step3: Analyze Option B

For the relation \(\{(- 1,6),(0,7),(5,11),(12,22)\}\), each x - value (\(-1\), \(0\), \(5\), \(12\)) is paired with exactly one y - value. So, this relation is a function.

Step4: Analyze Option C

For the relation \(\{(0,3),(6,7),(1,9),(4,16)\}\), each x - value (\(0\), \(6\), \(1\), \(4\)) is paired with exactly one y - value. So, this relation is a function.

Step5: Analyze Option D

For the relation \(\{(-1,3),(-5,10),(5,6),(1,-1)\}\), each x - value (\(-1\), \(-5\), \(5\), \(1\)) is paired with exactly one y - value. So, this relation is a function.

Answer:

A. \(\{(1,2),(1,3),(1,4),(1,5)\}\)