Final answer:
A rational function can cross a horizontal asymptote but not a vertical asymptote. The behavior of a rational function may change as it approaches infinity, allowing it to intersect a horizontal asymptote. However, a rational function cannot cross a vertical asymptote because it represents values where the denominator becomes zero.
Step-by-step explanation:
A rational function can cross a horizontal asymptote because the function's behavior may change as it approaches infinity or negative infinity. As the degree of the numerator and denominator of the rational function increase, the graph of the function may intersect the horizontal asymptote at certain points.
On the other hand, a rational function cannot cross a vertical asymptote because the vertical asymptote represents values where the denominator of the rational function becomes zero. Division by zero is undefined, so the function cannot cross a vertical asymptote.