Question

functions - table
state whether each table of values represents a function.
1)

x	y
-12	2
-10	10
0	-2
5	-6
8	-11
15	-15

2)

x	y
9	-18
-20	5
-6	1
-17	16
9	17
11	19

3)

x	y
4	-20
1	-17
4	-14
16	5
10	0
-19	-16

4)

x	y
-15	18
-11	18
-14	18
-9	18
-1	18
-5	18

5)

x	y
2	15
3	12
6	-4
7	-1
18	-4
20	-8

6)

x	y
-13	-3
-3	7
12	-13
17	8
-3	14
0	-19

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 for each table if any x - value is repeated with a different y - value.

Step2: Analyze Table 1)

• Check x - values: - 12, - 10, 0, 5, 8, 15. All x - values are unique. So each x has one y. So it is a function.

Step3: Analyze Table 2)

• Check x - values: 9, - 20, - 6, - 17, 9, 11. The x - value 9 appears twice with different y - values (- 18 and 17). So it is not a function.

Step4: Analyze Table 3)

• Check x - values: 4, 1, 4, 16, 10, - 19. The x - value 4 appears twice with different y - values (- 20 and - 14). So it is not a function.

Step5: Analyze Table 4)

• Check x - values: - 15, - 11, - 14, - 9, - 1, - 5. All x - values are unique (even though y - values are same, a function allows multiple inputs to have same output). So each x has one y. So it is a function.

Step6: Analyze Table 5)

• Check x - values: 2, 3, 6, 7, 18, 20. All x - values are unique (6 and 18 have same y, but that's allowed). So each x has one y. So it is a function.

Step7: Analyze Table 6)

• Check x - values: - 13, - 3, 12, 17, - 3, 0. The x - value - 3 appears twice with different y - values (7 and 14). So it is not a function.

Answer:

1. Function
2. Not a Function
3. Not a Function
4. Function
5. Function
6. Not a Function