Worksheet for identifying functions from various representations including tables, mappings, and ordered pairs.

Explanation:
We need to check each relation and decide whether it is a function.
A relation is a function if every input (x-value) has exactly one output (y-value).
If any x-value appears more than once with different y-values, it’s not a function.

Let’s go one by one:

1. Diagram:
x → y
2 → –2
3 → –3
4 → –4
5 → –5
Each x appears once → ✔ Function

2. Table:
x = –4 → y = 5
x = –3 → y = 5
x = –3 → y = 1
Here, x = –3 maps to both 5 and 1 → ✘ Not a function

3. Ordered pairs: (2, 8), (1, 12), (–1, 14), (3, 10)
All x-values: 2, 1, –1, 3 — all unique → ✔ Function

4. Ordered pairs: (4, –5), (5, –8), (6, –11), (6, –12)
x = 6 appears twice, with y = –11 and y = –12 → ✘ Not a function

5. Diagram:
x = 3 → y = 10
x = 6 → y = 10
x = 9 → y = 15
Each x appears once → ✔ Function
(Note: same y-values are okay — only repeated x with different y matters)

6. Table:
x = 8 → y = 12
x = 9 → y = 14
x = 10 → y = 15
x = 10 → y = 20
x = 10 appears twice with different y-values → ✘ Not a function

7. Ordered pairs: (–6, 4), (2, 4), (0, 4), (4, 4)
x-values: –6, 2, 0, 4 — all unique → ✔ Function
(All have same y = 4 — that’s fine!)

8. Table:
x = 10 → y = –6
x = 11 → y = –5
x = 12 → y = –4
All x-values unique → ✔ Function

9. Diagram:
x = –1 → y = 0
x = 3 → y = –4
x = 5 → y = –6
Wait — also x = 3 → y = –6? Let's look carefully:
Arrows show:
–1 → 0
3 → –4
3 → –6? No — actually, the diagram shows:
From x = 3, two arrows? Let me re-read:
The diagram says:
x side: –1, 3, 5
y side: 0, –4, –6, –8
Arrows:
–1 → 0
3 → –4
3 → –6? Hmm — the image shows three arrows from x-values to y-values.
But in standard interpretation of such diagrams, if an x has more than one arrow, it’s not a function.
Looking at #9: x = 3 has two arrows: one to –4 and one to –6.
Yes — that’s clear from the visual: two arrows from 3.
So x = 3 maps to two different y-values → ✘ Not a function

10. Diagram:
x = –30 → 20
x = 16 → 20
x = 35 → 20
Each x appears once → ✔ Function
(Multiple x’s can map to same y — okay!)

11. Table:
x = 8 → y = –3
x = 6 → y = 2
x = 7 → y = 0
x = 6 → y = –2
x = 6 appears twice: y = 2 and y = –2 → ✘ Not a function

12. Ordered pairs: (12, –3), (23, –6), (12, –4), (15, 0)
x = 12 appears twice: y = –3 and y = –4 → ✘ Not a function

Now summarize which are functions (✓) and which are not (✗):

1. ✓
2. ✗
3. ✓
4. ✗
5. ✓
6. ✗
7. ✓
8. ✓
9. ✗
10. ✓
11. ✗
12. ✗

So the final answers are marks under each relation:
1: ✓
2: ✗
3: ✓
4: ✗
5: ✓
6: ✗
7: ✓
8: ✓
9: ✗
10: ✓
11: ✗
12: ✗

Final Answer:
1: ✓, 2: ✗, 3: ✓, 4: ✗, 5: ✓, 6: ✗, 7: ✓, 8: ✓, 9: ✗, 10: ✓, 11: ✗, 12: ✗