Given the function:

$f(x) = \frac{x^4}{x^2 + 2}$

To find the vertical asymptotes, we need to determine the values of $x$ that make the denominator equal to zero. Vertical asymptotes occur where the denominator is zero and the numerator is non-zero.

Step 1: Set the denominator equal to zero

$x^2 + 2 = 0$

Step 2: Solve for $x$

$x^2 = -2$

$x = \sqrt{-2}$

Since the square root of a negative number is not a real number, there are no real values of $x$ that make the denominator zero. Therefore, the function does not have any vertical asymptotes.

Conclusion:

The correct answer is: B. There are no vertical asymptotes.

Would you like further details, or do you have any questions?

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Here are 5 related questions for further exploration:

1. What are horizontal asymptotes and how do you find them?
2. How can you determine the behavior of $f(x)$ near vertical asymptotes?
3. What is the significance of a hole in a function?
4. How do you find oblique asymptotes in a rational function?
5. What happens if both the numerator and denominator equal zero at the same point?

Tip: When dealing with rational functions, always check if the denominator can be zero to find vertical asymptotes.