The correct answer is:

D. If the numerator has a larger degree than the denominator, there is no horizontal asymptote. If the numerator has a smaller degree than the denominator, there is a horizontal asymptote at $y = 0$. If the numerator and denominator have the same degree, there is a horizontal asymptote at $y = \frac{a}{b}$, where $a$ and $b$ are the leading coefficients of the numerator and denominator, respectively. Therefore, there is at most one horizontal asymptote.

Explanation:

A horizontal asymptote is related to the end behavior of the rational function as $x \to \infty$ or $x \to -\infty$. The number of horizontal asymptotes depends on the degrees of the numerator and denominator of the rational function:

1. Degree of numerator < Degree of denominator: The horizontal asymptote is $y = 0$.
2. Degree of numerator = Degree of denominator: The horizontal asymptote is $y = \frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}}$.
3. Degree of numerator > Degree of denominator: There is no horizontal asymptote, though the graph may have an oblique (slant) asymptote.

Thus, a rational function can have at most one horizontal asymptote.

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Would you like more details or have any questions on this topic?

Follow-up questions:

1. What happens if the numerator has a degree exactly one higher than the denominator?
2. How can you determine if a rational function has a slant asymptote?
3. How do vertical asymptotes differ from horizontal asymptotes in rational functions?
4. Can a rational function cross its horizontal asymptote?
5. How does the behavior of a rational function near infinity affect its horizontal asymptote?

Tip: Horizontal asymptotes describe end behavior, not necessarily the behavior of the graph near the origin or at specific points!