Question

How to determine if a function is rational?

a) If it has whole numbers only
b) If it has a fractional exponent
c) If it has variables in the denominator
d) If it has integer coefficients

Answer 1

A function is rational if it can be expressed as the quotient of two polynomials, meaning it has variables in the denominator. Options involving whole numbers, fractional exponents, or integer coefficients alone do not define a rational function. The correct option is C.

Step-by-step explanation:

To determine if a function is rational, the key characteristic to look for is if the function can be expressed as the quotient of two polynomials, that is, one polynomial divided by another. Therefore, the correct answer to the question is c) If it has variables in the denominator. This means that for a function to be rational, the denominator must have a polynomial, which may include variables. It is not sufficient for a function to have whole numbers only, fractional exponents, or integer coefficients to be classified as a rational function.

When analyzing rational functions, you can follow these guidelines:

1. Eliminate terms wherever possible to simplify the algebra.
2. Check the answer to see if it is reasonable.