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A graph is shown in the below figure, ∘ symbol signifies that the straight line does not touch the point and the ∙ symbol signifies that the line touches the point. Choose the correct option(s)
The graph represents the graph of neither even function nor odd function.

The graph represents the graph of either even function or odd function.

The graph cannot be of a function, because it passes the vertical line test but fails the horizontal line test.

The graph can be of a function, because it passes the vertical line test.

The graph cannot be of a function, because it passes the horizontal line test but fails the vertical line test.

Let's analyze the graph step-by-step to choose the correct options from the given statements.

1. **Vertical Line Test**: This test helps us determine if the graph represents a function. If a vertical line intersects the graph at more than one point, it means that for a given \( x \)-value, there is more than one \( y \)-value, and thus, the graph is not a function. In this case, each vertical line intersects the graph at exactly one point, so it **passes the vertical line test**. Therefore, the graph can represent a function.

2. **Horizontal Line Test**: This test is used to determine if a function is one-to-one (meaning each \( y \)-value has a unique \( x \)-value). In this graph, certain horizontal lines intersect the graph at multiple points, meaning it **fails the horizontal line test**. This implies the function is not one-to-one.

3. **Even or Odd Function**: A function is even if it is symmetric about the y-axis (i.e., \( f(x) = f(-x) \)), and it is odd if it has origin symmetry (i.e., \( f(-x) = -f(x) \)). Observing the graph, it does not exhibit symmetry about the y-axis or the origin. Therefore, it is **neither an even nor an odd function**.

### Conclusion
The correct answers are:

- **The graph can be of a function, because it passes the vertical line test.**
- **The graph represents the graph of neither even function nor odd function.**

Would you like further explanation on any of these points? 

Here are some additional questions to deepen your understanding:

1. How does the horizontal line test differ in purpose from the vertical line test?
2. What would make a function one-to-one, and why is that significant?
3. What characteristics must a graph have to represent an even function?
4. Can a function be both even and odd? If so, what is an example?
5. Why is passing the vertical line test essential for a graph to represent a function?

**Tip:** Understanding the vertical and horizontal line tests helps in determining if a graph represents a function and whether it's one-to-one.

A graph is shown in the below figure, ∘ symbol signifies that the straight line does not touch the point and the ∙ symbol signifies that the line touches the point. Choose the correct option(s). The graph represents the graph of neither even function nor odd function. The graph represents the graph of either even function or odd function. The graph cannot be of a function, because it passes the vertical line test but fails the horizontal line test. The graph can be of a function, because it passes the vertical line test. The graph cannot be of a function, because it passes the horizontal line test but fails the vertical line test.

Explore the analysis of a given graph based on vertical and horizontal line tests. This problem examines whether the graph represents an even or odd function and determines if it can represent a function. Suitable for students in Grades 10-12.

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