This math topic focuses on identifying the domain of functions where the numerator is an integer and the denominator is a quadratic expression with complex roots. Each question presents a function in the form \( \frac{a}{bx^2 + cx + d} \), requiring students to determine the set of all possible x-values (domain) that will make the function defined. Solutions involve analyzing whether the quadratic denominator has any real roots that might lead to discontinuities. The student's understanding of complex roots and their impact on the domain of a function is assessed, and responses are visualized using number line diagrams to depict the domain.

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Function Domain - Fraction Integer over Quadratic (Complex Roots) to Number Line

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What number line shows the domain of this function?

f(x)=35x2+3x1f(x) = \frac{-3}{-5x^2+3x-1}

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