This math topic focuses on determining the domains of functions where the functions are formed by a linear numerator over the square root of a quadratic denominator. Specifically, the worksheet handles cases where the quadratic has complex roots. Students are required to determine the correct domain from given number line options for each function scenario. The goal is to visualize and solve for function domains that are influenced by complex roots, integrating algebraic function analysis with geometric representation on number lines. This is categorized under practice in functions domain and range solving.

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Function Domain - Fraction Linear over Root of Quadratic (Complex Roots) to Number Line

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What number line shows the domain of this function?

f(x)=1x44x26x+21f(x) = \frac{1x-4}{\sqrt{4x^2-6x+21}}

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