Functions - Graphing worksheet with multiple-choice questions on identifying function graphs.

Problem Analysis:

The task involves determining whether each graph represents a function. A function is defined as a relation where each input (x-value) corresponds to exactly one output (y-value). To determine if a graph represents a function, we use the vertical line test: If any vertical line intersects the graph at more than one point, the graph does not represent a function.

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Part A: State whether each graph represents a function.

We will analyze each graph individually using the vertical line test.

#### 1. Graph (a)
- Description: The graph is a parabola opening upwards.
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

#### 2. Graph (b)
- Description: The graph is another parabola opening upwards.
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

#### 3. Graph (c)
- Description: The graph is a circle.
- Vertical Line Test: A vertical line can intersect the circle at two points (e.g., near the center).
- Conclusion: This graph does not represent a function.

#### 4. Graph (d)
- Description: The graph is a straight line with a positive slope.
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

#### 5. Graph (e)
- Description: The graph is a V-shaped figure (absolute value function).
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

#### 6. Graph (f)
- Description: The graph is a sideways parabola (opening to the right).
- Vertical Line Test: A vertical line can intersect this graph at two points.
- Conclusion: This graph does not represent a function.

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Part B: Which of the following graphs represents a function?

We will analyze each graph individually using the vertical line test.

#### 1. Graph (i)
- Description: The graph is a curve that resembles a cubic function.
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

#### 2. Graph (ii)
- Description: The graph is a parabola opening downwards.
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

#### 3. Graph (iii)
- Description: The graph is a sine wave.
- Vertical Line Test: Any vertical line drawn on this graph will intersect it at most once.
- Conclusion: This graph represents a function.

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Final Answers:

#### Part A:
1. (a) Function
2. (b) Function
3. (c) Not a function
4. (d) Function
5. (e) Function
6. (f) Not a function

#### Part B:
1. (i) Function
2. (ii) Function
3. (iii) Function

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Boxed Final Answer:

\[
\boxed{
\text{Part A: (a) Yes, (b) Yes, (c) No, (d) Yes, (e) Yes, (f) No}
}
\]
\[
\boxed{
\text{Part B: (i) Yes, (ii) Yes, (iii) Yes}
}
\]