# Which is a rational function? a) Y = \frac{x - 3}{x^2} \\ b) Y = 2x \\ c) Y = \frac{x - 5}{2} \\...

## Question:

Which is a rational function?

{eq}a) Y = \frac{x - 3}{x^2} \\ b) Y = 2x \\ c) Y = \frac{x - 5}{2} \\ d) Y = x^2 - x + 4 {/eq}

## Rational Function

A specific type of function called a rational function has a very specific form. The form of a rational function is a quotient, specifically of two polynomials, and the denominator must contain our variable at least once. These types of functions may have horizontal and/or vertical asymptotes.

Let's analyze these four functions so that we can declare which of the four is a rational function.

a) This function is the quotient of a linear term and a quadratic monomial. Since a rational function is expressed as the quotient of two polynomials, this fits the definition. Therefore, this is the rational function.

b) The function in this part is linear, as we have a coefficient times x. This is not a rational function, since it's not a quotient.

c) While this function is a quotient, the denominator is a constant. For this to be a rational function, the denominator would need to contain our variable. Therefore, this is not actually a rational function.

d) Once again, this is not a rational function since it doesn't have a denominator containing x. Instead, it's a polynomial, as we have only the sum and difference of terms containing our variable to a positive integer power.