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Let's analyze the graphs to determine which functions are neither even nor odd.

1. **Even functions** satisfy \( f(x) = f(-x) \) for all \( x \). This means their graphs are symmetric about the y-axis.
2. **Odd functions** satisfy \( f(x) = -f(-x) \) for all \( x \). Their graphs are symmetric about the origin.

### Analysis of each graph:

- **Graph I**: 
  This function does not exhibit symmetry about the y-axis or origin. Therefore, it is neither even nor odd.

- **Graph II**: 
  The graph appears symmetric about the y-axis. This makes it an even function.

- **Graph III**: 
  This graph exhibits symmetry about the origin, indicating it is an odd function.

- **Graph IV**: 
  The graph does not show symmetry about the y-axis or the origin. Thus, it is neither even nor odd.

### Conclusion:
The functions that are neither odd nor even are **I and IV**.

The correct answer is **I and IV**.

Would you like more details or explanations? Here are five related questions to consider:

1. How can you algebraically test if a function is even or odd?
2. What type of symmetry does an odd function have?
3. Can a function be both even and odd?
4. What are the properties of a function that is neither odd nor even?
5. How does symmetry help in classifying a function?

**Tip**: Always check for symmetry with respect to the y-axis for even functions and symmetry about the origin for odd functions.

Which of the following are neither odd nor even functions?

Analyze graphs to determine which functions are neither odd nor even. This exercise covers the concept of even and odd functions and involves identifying symmetry with respect to the y-axis and the origin. Suitable for high school students in Grades 9-12.

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