Which statement describes a rational function?

Which statement describes a rational function?

• A. It is a ratio of two polynomial expressions with q(x) ≠ 0
• B. It is sin(x) divided by cos(x)
• C. It has only constant terms
• D. It cannot be evaluated at any x

Answer: (A)

Rational functions are formed as the ratio of two polynomials, with the denominator not equal to zero wherever you evaluate the function. This statement matches that idea because it describes a ratio of two polynomial expressions and explicitly requires the denominator q(x) to be nonzero, which ensures the function is defined at the x-values you test. The other options don’t fit this exact idea: a ratio like sin(x) over cos(x) uses trigonometric functions rather than polynomials, so it isn’t a rational function in the standard algebraic sense; having only constant terms describes a constant function, not a ratio of polynomials; and saying it cannot be evaluated at any x goes against the usual notion that a rational function is defined for many x values except where the denominator happens to be zero.

Rational functions are formed as the ratio of two polynomials, with the denominator not equal to zero wherever you evaluate the function. This statement matches that idea because it describes a ratio of two polynomial expressions and explicitly requires the denominator q(x) to be nonzero, which ensures the function is defined at the x-values you test. The other options don’t fit this exact idea: a ratio like sin(x) over cos(x) uses trigonometric functions rather than polynomials, so it isn’t a rational function in the standard algebraic sense; having only constant terms describes a constant function, not a ratio of polynomials; and saying it cannot be evaluated at any x goes against the usual notion that a rational function is defined for many x values except where the denominator happens to be zero.