Question

1 which relation is a function? a (1,0), (3,0), (1,1), (3,1), (1,3) b (1,1), (2,2), (3,3), (4,4), (5,8) c (2,7), (6,5), (4,4), (3,3), (2,1) d (9, -3), (9, 3), (4, -2), (4, 2), (0, 0)

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 in Option A: \((1,0),(3,0),(1,1),(3,1),(1,3)\)
The x - value \(1\) is paired with \(0\), \(1\), and \(3\) (different y - values), and the x - value \(3\) is paired with \(0\) and \(1\) (different y - values). So, this relation is not a function.

Step3: Analyze Option B

For the relation in Option B: \((1,1),(2,2),(3,3),(4,4),(5,8)\)
Each x - value (\(1\), \(2\), \(3\), \(4\), \(5\)) is paired with exactly one y - value. So, this relation is a function.

Step4: Analyze Option C

For the relation in Option C: \((2,7),(6,5),(4,4),(3,3),(2,1)\)
The x - value \(2\) is paired with \(7\) and \(1\) (different y - values). So, this relation is not a function.

Step5: Analyze Option D

For the relation in Option D: \((9, - 3),(9,3),(4,-2),(4,2),(0,0)\)
The x - value \(9\) is paired with \(-3\) and \(3\) (different y - values), and the x - value \(4\) is paired with \(-2\) and \(2\) (different y - values). So, this relation is not a function.

Answer:

B. \((1,1),(2,2),(3,3),(4,4),(5,8)\)