First of all, let's define the properties of rational functions that we're interested in. A rational function has exactly one vertical asymptote when the degree of the denominator is one greater than the degree of the numerator. A rational function has a horizontal asymptote at y=0 when the degree of the denominator is greater than the degree of the numerator. A rational function will have holes where common factors in the numerator and denominator can be canceled out.
Now, let's look at each function one by one:
A. The degree of the numerator and denominator is the same (both are 2nd degree), therefore it does not have a vertical asymptote.
B. The degree of the numerator and denominator is the same (both are 2nd degree), therefore it does not have a vertical asymptote.
C. The degree of the denominator is greater than the degree of the numerator (2nd degree vs 1st degree), thus, it has one vertical asymptote. The function (2x - 5) / (x^2 - 1) can be factored as (2x - 5) / ((x - 1)(x + 1)). There are no common factors that can be canceled out, so this function has no holes. And since the degree of the denominator is greater than that of the numerator, there is a horizontal asymptote at y=0.
D. The degree of the numerator and denominator is the same (both are 1st degree), therefore it does not have a vertical asymptote.
Hence, option C is the correct answer. The function (2x - 5) / (x^2 - 1) meets all the given criteria having exactly one vertical asymptote, no holes, and a horizontal asymptote of y=0.