Finding Domain of Rational Functions

Pre-Calculus · Axiom Academy

EXAMPLE Finding Domain of Rational Functions Work through where a rational function is undefined by hunting the zeros of its denominator. Find the domain of the rational function . Nicely done — you found the domain of a rational function by tracking down exactly where the denominator hits zero. Find the trouble spots: the only thing that can break a rational function is division by zero, so set the denominator equal to zero. Factor, then solve: x^2 - x - 6 = (x + 2)(x - 3) , and the zero product property gives x = -2 and x = 3 . Exclude, don't include: those zeros are removed from the domain — the numerator never restricts the domain. Same recipe every time: factor the denominator, set it to zero, and exclude the solutions. The rest of the real line is fair game.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.