Regarding a rational function f(x) = p(x)/q(x), what must be true for the function to be defined?

Regarding a rational function f(x) = p(x)/q(x), what must be true for the function to be defined?

• A. q(x) cannot equal 0
• B. q(x) must equal zero
• C. q(x) must be a constant nonzero
• D. q(x) must be a polynomial of degree 2

Answer: (A)

A rational function is defined only where the denominator isn't zero, because division by zero is undefined. So the key requirement is that q(x) does not equal zero for the x-values in question. If q(x) ever equals zero, that x is excluded from the domain. The other statements add unnecessary restrictions (denominator must be a constant, or must have a specific degree); they aren’t required. In short, the function is defined exactly on the set of x where q(x) ≠ 0.

A rational function is defined only where the denominator isn't zero, because division by zero is undefined. So the key requirement is that q(x) does not equal zero for the x-values in question. If q(x) ever equals zero, that x is excluded from the domain. The other statements add unnecessary restrictions (denominator must be a constant, or must have a specific degree); they aren’t required. In short, the function is defined exactly on the set of x where q(x) ≠ 0.