True. A rational function might cross through a horizontal asymptote.
A rational function is a function that can be expressed as the quotient of two polynomial functions, where the denominator is not equal to zero. Rational functions can have vertical asymptotes, where the function approaches infinity or negative infinity as it approaches a certain value of x, and horizontal asymptotes, where the function approaches a constant value as x approaches positive or negative infinity.
It is possible for a rational function to cross through a horizontal asymptote. This occurs when the degree of the numerator is less than the degree of the denominator. In this case, the function will approach the horizontal asymptote as x approaches positive or negative infinity, but it will cross through the asymptote at least once.
For example, consider the rational function f(x) = (x^2 - 1)/(x + 1). The degree of the numerator is 2 and the degree of the denominator is 1. The horizontal asymptote is y = x - 1, since as x approaches positive or negative infinity, f(x) approaches x - 1. However, f(x) crosses through this asymptote at x = -2.
Therefore, it is true that a rational function might cross through a horizontal asymptote.