The graph provided shows a periodic function plotted between $-2\pi$ and $2\pi$ on the x-axis. The question asks if this function is even, odd, or neither.

Key Concepts:

• Even Function: A function is even if it is symmetric about the y-axis, meaning $f(-x) = f(x)$.
• Odd Function: A function is odd if it has rotational symmetry about the origin, meaning $f(-x) = -f(x)$.
• Neither: If the function satisfies neither of these conditions, it is classified as neither even nor odd.

Analysis:

Looking at the graph:

1. The function appears to have symmetry about the y-axis, meaning that the left-hand side of the graph mirrors the right-hand side. This is characteristic of even functions.
2. The function does not exhibit rotational symmetry about the origin, which would indicate an odd function.

Conclusion:

Visually, the function is even, based on its symmetry about the y-axis.

The correct answer is:

• A. Even

Would you like a detailed explanation of how to test functions for even or odd behavior algebraically? Or do you have any other questions?

5 Relative Questions:

1. How can you determine if a function is even or odd from its algebraic formula?
2. What are the main characteristics of even functions beyond symmetry?
3. Can a function be both even and odd?
4. How do periodic functions relate to even and odd properties?
5. What is the significance of symmetry in real-world applications of functions?

Tip:

When analyzing functions visually, always check for symmetry to determine whether it is even, odd, or neither. Symmetry about the y-axis usually indicates an even function, while rotational symmetry about the origin suggests an odd function.