To analyze the function in the given graph and determine whether it is even, odd, or neither, let's proceed step by step:

Observations from the graph:

1. Even Function: A function $f(x)$ is even if its graph is symmetric with respect to the $y$-axis. That is, $f(-x) = f(x)$ for all $x$ in the domain.
2. Odd Function: A function $f(x)$ is odd if its graph is symmetric with respect to the origin. That is, $f(-x) = -f(x)$ for all $x$ in the domain.
3. Neither: If the function does not follow either symmetry, it is classified as neither.

Symmetry Analysis:

• The graph is symmetric with respect to the y-axis. For every point $(x, y)$, there is a corresponding point $(-x, y)$.
• This indicates that $f(-x) = f(x)$, which is the definition of an even function.

Conclusion:

The given function is even.

Do you want a detailed explanation or help identifying similar functions?

Here are 5 follow-up questions related to this analysis:

1. How can we mathematically verify if a function is even or odd using its equation?
2. What are some common examples of even functions, such as $x^2$ or $\cos(x)$?
3. Can a function be both even and odd? If not, why?
4. How would symmetry with respect to the origin look in a graph?
5. How do periodic properties, like those in this graph, relate to symmetry?

Tip: Always check for symmetry using test points on either side of the y-axis to confirm a function's even or odd nature visually.