To determine whether the function $f(x) = x^4 - 4x^2 + 9$ is even, odd, or neither, we need to apply the definitions of even and odd functions.

• A function $f(x)$ is even if $f(-x) = f(x)$ for all $x$.
• A function $f(x)$ is odd if $f(-x) = -f(x)$ for all $x$.

Step 1: Check if the function is even

Let's compute $f(-x)$:

$f(-x) = (-x)^4 - 4(-x)^2 + 9 = x^4 - 4x^2 + 9$

Since $f(-x) = f(x)$, the function satisfies the condition for being even.

Conclusion:

The function is even.

So the correct answer is B. The function is even.

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Would you like more details or have any questions? Here's a list of related topics that might interest you:

1. What makes a function even or odd?
2. Can a function be both even and odd?
3. How do polynomial functions behave in terms of evenness and oddness?
4. What is the significance of symmetry in even and odd functions?
5. How can you determine whether a trigonometric function is even or odd?

Tip: To determine whether a polynomial is even, check the exponents of each term. If all exponents are even, the function is likely even.