This math unit focuses extensively on analyzing and determining the domain of various functions involving fractions with numerators and denominators that include quadratic expressions and their roots. Initially, students engage in identifying the domains of functions with quadratic denominators, both with real and complex roots, utilizing number lines and set notation to express these domains. As the unit progresses, complexities increase with the introduction of radical expressions in the denominators and numerators, challenging students to consider additional constraints like the non-negativity of radicands (expressions under square roots) and ensuring denominators are non-zero. The skills evolve from simple domain identification on number lines to more nuanced definitions involving complex roots and square roots, requiring a deeper understanding of function behavior and restrictions, particularly in the context of real and complex numbers. Students learn to map accurate domain representations and handle functions with various root conditions, enhancing their problem-solving abilities in algebraic contexts.Skills you will learn include:
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