Worksheet identifying functions from various representations including tables, graphs, and sets of points.

Let's go through each of the 12 items in your "Function or Not a Function?" worksheet and determine whether each represents a function or not a function, based on the definition of a function:

> A function is a relation where each input (x-value) has exactly one output (y-value).
> If any input maps to more than one output, it's not a function.

We'll analyze each item one by one.

---

#1: Table

```
Domain | Range
4 | 3
5 | 4
2 | 5
4 | 6
```

- Input `4` appears twice: once with output `3`, once with output `6`.
- So, one input (4) → two outputs → Not a function

✔ Answer: NOT a function

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#2: Graph (Vertical Line Test)

This is a graph with points plotted:
- Points: (−2, −1), (−1, 0), (0, 1), (1, 2), (2, 3)
- It's a straight line going up.
- Apply vertical line test: Any vertical line crosses only one point.

✔ Answer: FUNCTION

---

#3: Graph (Curve)

It's a parabola opening downward (like a hill).
- This is a standard quadratic graph.
- Vertical line test: Every vertical line hits only one point.

✔ Answer: FUNCTION

---

#4: Set of ordered pairs

{(−1, −2), (0, 1), (1, 4), (3, 7)}

- Each x-value is unique: −1, 0, 1, 3 → all different.
- No repeated inputs → each input has one output.

✔ Answer: FUNCTION

---

#5: Mapping Diagram

Input: −1, 0, 2
Output: −1, 1, 2, 3, 4

- Arrows:
- −1 → −1
- 0 → 1 and 2? Wait — looks like 0 maps to both 1 and 2
- 2 → 3 and 4?

Wait — let’s check carefully.

From diagram:
- −1 → −1 (only one)
- 0 → 1 and 2 → two outputs for same input
- 2 → 3 and 4 → again, two outputs

So input 0 has two outputs, and input 2 has two outputs.

✘ Answer: NOT a function

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#6: Graph (Grid with points)

Points shown: (−2, 1), (−1, 2), (0, 3), (1, 4), (2, 5)

- These form a straight line.
- All x-values are distinct.
- Vertical line test passes.

✔ Answer: FUNCTION

---

#7: Table

```
x | y
1 | 1
2 | 2
3 | 4
3 | 4
```

- x = 3 appears twice, but both times y = 4 → same output.
- So even though it repeats, it's still one output per input.
- The definition allows multiple entries as long as the mapping is consistent.

✔ Answer: FUNCTION

(Note: Duplicate rows are okay if they represent same input-output pair.)

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#8: Set of ordered pairs

{(1,1), (1,2), (2,1), (2,2)}

- Input 1 → outputs 1 and 2 → two outputs
- Input 2 → outputs 1 and 2 → two outputs

So multiple outputs for same input → violates function rule.

✘ Answer: NOT a function

---

#9: Mapping Diagram

Input: 1, 2, 5
Output: 2, 3, 5

Arrows:
- 1 → 2
- 2 → 3
- 5 → 5

Each input has exactly one output.

✔ Answer: FUNCTION

---

#10: Set of ordered pairs

{(4, −2), (4, −1), (1, 1), (4, 2)}

- Input 4 appears three times: outputs −2, −1, 2 → multiple outputs for x=4
- So one input → multiple outputs

✘ Answer: NOT a function

---

#11: Table

```
x | y
0 | 2
−1 | 1
−2 | 3
0 | −2
2 | −4
```

- x = 0 appears twice: first with y=2, then y=−2
- So input 0 has two different outputs → not a function

✘ Answer: NOT a function

---

#12: Graph (Wavy Curve)

Looks like a sine wave or oscillating curve.

- Use vertical line test: Draw a vertical line anywhere — it will cross the graph at multiple points (e.g., multiple y-values for same x).

→ So fails vertical line test

✘ Answer: NOT a function

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✔ Final Answers Summary:

| # | Is it a Function? |
|---|-------------------|
| 1 | ✘ No |
| 2 | ✔ Yes |
| 3 | ✔ Yes |
| 4 | ✔ Yes |
| 5 | ✘ No |
| 6 | ✔ Yes |
| 7 | ✔ Yes |
| 8 | ✘ No |
| 9 | ✔ Yes |
|10 | ✘ No |
|11 | ✘ No |
|12 | ✘ No |

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🔍 Key Takeaways:

- Function: Each input has only one output.
- Not a function: If any input has more than one output.
- For graphs, use the vertical line test.
- For tables/mappings, check for duplicate inputs with different outputs.

Let me know if you'd like this formatted as a printable answer sheet!