Question

2 which of the following relations is a function?
a.

x	y
0	1
2	4
4	4
6	1

b.

x	y
3	1
6	2
8	3
8	4

c.

x	y
2	3
2	5
2	6
2	8

d.

x	y
1	3
1	4
3	5
5	6

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze Option A

In option A, the x - values are 0, 2, 4, 6. Each x - value appears only once. So for x = 0, y = 1; x = 2, y = 4; x = 4, y = 4; x = 6, y = 1. No x - value is repeated with different y - values.

Step3: Analyze Option B

In option B, the x - value 8 appears twice, with y - values 3 and 4. So the input 8 has two different outputs, so it is not a function.

Step4: Analyze Option C

In option C, the x - value 2 appears four times, with different y - values (3, 5, 6, 8). So the input 2 has multiple outputs, so it is not a function.

Step5: Analyze Option D

In option D, the x - value 1 appears twice, with y - values 3 and 4. So the input 1 has two different outputs, so it is not a function.

Answer:

A.

x	y
2	4
4	4
6	1