https://file.aiquickdraw.com/mathbot/file/17272835469599qhiu9qt.jpg

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?

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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!

Which of the following is true about the function f(x)? The graph depicts a polynomial symmetric about the y-axis, which suggests it may be even or odd.

This question asks students to determine if a polynomial function is even, odd, or neither by analyzing the graph's symmetry. Symmetry about the y-axis indicates the function is even. This topic is crucial for students learning about polynomial behavior and function properties in Grades 9-12.

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