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.