To determine whether the function \( y = f(x) \) is even, odd, or neither, you need to apply the following conditions:

1. **Even Function**: A function is even if \( f(-x) = f(x) \) for all \( x \). This means that the graph of the function is symmetric about the y-axis.

2. **Odd Function**: A function is odd if \( f(-x) = -f(x) \) for all \( x \). This means that the graph of the function is symmetric about the origin.

3. **Neither**: If neither of the above conditions is satisfied, the function is neither even nor odd.

### Steps to classify:
1. Compute \( f(-x) \) for the function.
2. Compare \( f(-x) \) with \( f(x) \) and check:
   - If \( f(-x) = f(x) \), it's even.
   - If \( f(-x) = -f(x) \), it's odd.
   - If neither is true, the function is neither even nor odd.

If you have a specific function, I can help you classify it.

Would you like to provide a specific function for further analysis?

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Here are 5 related questions for further exploration:
1. What does it mean graphically if a function is even or odd?
2. Can a function be both even and odd?
3. How does the domain of a function affect whether it's even or odd?
4. Are there specific families of functions that are always even or odd?
5. What happens when you add or multiply even and odd functions?

**Tip**: Testing the parity of a polynomial function can often be done by looking at the powers of \( x \) in each term.

Learn how to determine whether a function is even, odd, or neither by applying symmetry conditions. Understand key concepts such as even function (f(-x) = f(x)) and odd function (f(-x) = -f(x)), along with examples. Suitable for students in Grades 9-12.

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