This math topic focuses on determining the domain of functions where the denominator includes a square root of a quadratic expression. Specifically, the problems deal with scenarios where the quadratic under the square root might have complex roots. The questions require students to illustrate the domain of such functions on a number line. This involves understanding complex roots of quadratics, constraints placed by square roots (e.g., the expression under the root must be non-negative), and the implications of these factors on the admissible values of the function’s input (domain). Each question presents a function and asks which number line correctly represents its domain.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.