Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which statement is true about a rational function?

1. It is a single polynomial expression

2. Its domain excludes values where the numerator equals 0

3. It is a fraction constructed by two polynomial expressions

4. It cannot have vertical asymptotes

The correct answer is: It is a fraction constructed by two polynomial expressions

A rational function is defined as a function that can be expressed as the quotient of two polynomial functions. This means that it can be written in the form \( f(x) = \frac{P(x)}{Q(x)} \), where both \( P(x) \) and \( Q(x) \) are polynomials. This definition supports the correctness of the answer provided, as it emphasizes the key characteristic of rational functions—their formation from two polynomial expressions. The concept also leads to other important properties, such as identifying points where the function can be undefined, particularly when the denominator equals zero, indicating potential vertical asymptotes in the graph of the function. Furthermore, rational functions can certainly have vertical asymptotes, specifically at points where the polynomial in the denominator is equal to zero, which further underscores the importance of the denominator in the behavior of rational functions. Understanding these aspects helps in grasping the broader characteristics and behaviors of rational functions within various mathematical contexts.