From the image, the graph depicts a polynomial function $f(x)$ which is symmetric about the y-axis. This symmetry indicates that $f(x)$ is an even function.

Explanation:

• A function is even if $f(-x) = f(x)$ for all $x$. Graphically, even functions are symmetric about the y-axis.
• A function is odd if $f(-x) = -f(x)$ for all $x$. Graphically, odd functions have rotational symmetry about the origin.

Since the graph is symmetric about the y-axis, the correct answer is:

• The function $f$ is an even function.

Would you like further explanation or details on even and odd functions?

Here are 5 related questions you can explore:

1. How can you algebraically determine if a function is even or odd?
2. What is the general form of an even function?
3. How does the degree of a polynomial affect whether it is even or odd?
4. What are some real-world examples of even and odd functions?
5. Can a function be both even and odd?

Tip: The symmetry of a function's graph can help quickly identify if it's even, odd, or neither!