Final answer:
The statement is true; a vertical asymptote occurs in a rational function when the denominator equals zero and the numerator is nonzero at that point, resulting in the function approaching infinity or negative infinity.
Step-by-step explanation:
The statement that a vertical asymptote of a rational function can occur only at a zero of its denominator as long as the numerator is nonzero is True. A vertical asymptote in a rational function, which is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials, occurs when the denominator q(x) is equal to zero and the numerator p(x) is not zero at the same point. The function approaches infinity or negative infinity as x approaches the zero of the denominator. It's important to remember, however, that if both the numerator and the denominator have a common factor that equals zero, this may result in a hole rather than an asymptote if the common factor is canceled out.