Worksheet for identifying functions using various representations.

To determine whether each given scenario represents a function or not, we need to apply the definition of a function: A relation is a function if and only if each element in the domain (input) is paired with exactly one element in the range (output). In other words, no input can be associated with more than one output.

Let's analyze each case step by step:

---

#1

- Domain: \( \{4, 3, 2, 4\} \)
- Range: \( \{5, 4, 5, 6\} \)

#### Analysis:
- The domain contains the value \(4\) twice.
- However, the corresponding outputs for \(4\) are different (\(5\) and \(6\)).
- This violates the definition of a function because the same input (\(4\)) is mapped to two different outputs.

Conclusion: Not a Function

---

#2

- Graph: A set of points on a coordinate plane.

#### Analysis:
- Each \(x\)-value (domain) appears only once.
- No vertical line would intersect the graph at more than one point (Vertical Line Test).
- Therefore, each input is paired with exactly one output.

Conclusion: Function

---

#3

- Graph: A parabolic curve.

#### Analysis:
- The graph passes the Vertical Line Test: No vertical line intersects the curve at more than one point.
- Each \(x\)-value corresponds to exactly one \(y\)-value.

Conclusion: Function

---

#4

- Input/Output Table:
- Input: \(-1, 0, 2\)
- Output: \(0, 1, 4\)

#### Analysis:
- Each input value is unique and maps to exactly one output value.
- There are no repeated inputs.

Conclusion: Function

---

#5

- Input/Output Table:
- Input: \(-1, 0, 2\)
- Output: \(0, 3, 4\)

#### Analysis:
- Each input value is unique and maps to exactly one output value.
- There are no repeated inputs.

Conclusion: Function

---

#6

- Graph: A sinusoidal wave.

#### Analysis:
- The graph passes the Vertical Line Test: No vertical line intersects the curve at more than one point.
- Each \(x\)-value corresponds to exactly one \(y\)-value.

Conclusion: Function

---

#7

- Table:
$$
\begin{array}{c|c}
x & y \\
\hline
0 & 0 \\
2 & -1 \\
2 & 1 \\
3 & 4 \\
\end{array}
$$

#### Analysis:
- The input \(2\) is paired with two different outputs (\(-1\) and \(1\)).
- This violates the definition of a function.

Conclusion: Not a Function

---

#8

- Set of Ordered Pairs:
$$
\{(1, 1), (3, 2), (2, 1), (1, 2)\}
$$

#### Analysis:
- The input \(1\) is paired with two different outputs (\(1\) and \(2\)).
- This violates the definition of a function.

Conclusion: Not a Function

---

#9

- Input/Output Table:
- Input: \(1, 2, 5\)
- Output: \(1, 4, 6\)

#### Analysis:
- Each input value is unique and maps to exactly one output value.
- There are no repeated inputs.

Conclusion: Function

---

#10

- Set of Ordered Pairs:
$$
\{(8, 3), (0, 3), (8, 0), (0, 1), (8, 2)\}
$$

#### Analysis:
- The input \(8\) is paired with three different outputs (\(3, 0, 2\)).
- This violates the definition of a function.

Conclusion: Not a Function

---

#11

- Input/Output Table:
- Input: \(-3, -2, 0, 1\)
- Output: \(3, 4, 0, -2\)

#### Analysis:
- Each input value is unique and maps to exactly one output value.
- There are no repeated inputs.

Conclusion: Function

---

#12

- Graph: A spiral curve.

#### Analysis:
- The graph passes the Vertical Line Test: No vertical line intersects the curve at more than one point.
- Each \(x\)-value corresponds to exactly one \(y\)-value.

Conclusion: Function

---

Final Answers:

$$
\boxed{
\begin{array}{cccc}
\text{#1: Not a Function} & \text{#2: Function} & \text{#3: Function} & \text{#4: Function} \\
\text{#5: Function} & \text{#6: Function} & \text{#7: Not a Function} & \text{#8: Not a Function} \\
\text{#9: Function} & \text{#10: Not a Function} & \text{#11: Function} & \text{#12: Function} \\
\end{array}
}
$$