From your uploaded image, it seems like you are working on identifying whether a function is Odd, Even, or Neither based on symmetry properties of the function's graph.

Key concepts:

1. Even functions:

   • Symmetrical about the y-axis.
   • $f(x) = f(-x)$.

2. Odd functions:

   • Symmetrical about the origin (rotational symmetry of 180°).
   • $f(-x) = -f(x)$.

3. Neither:

   • If a function does not exhibit either symmetry.

Analyzing the Graphs:

1. First Graph:

   • The graph can be rotated 180° about the origin and still appear the same.
   • This indicates it is an odd function.
   • Correct answer: Odd.

2. Second Graph:

   • The graph is symmetrical about the y-axis.
   • This indicates it is an even function.
   • Correct answer: Even.

It seems the selections made in the example provided are incorrect because the symmetry of the graphs was not properly identified.

Would you like a more detailed explanation of these properties or help with additional examples?

5 Related Questions:

1. How can you algebraically verify if a function is even or odd?
2. Can a function be both even and odd? Why or why not?
3. How does rotational symmetry help in identifying odd functions?
4. Are there real-world examples of even or odd functions?
5. How can the concept of symmetry be applied in solving equations?

Tip:

Always test $f(x) = f(-x)$ and $f(-x) = -f(x)$ algebraically to confirm even or odd status, especially when the graph is unclear.