This math topic focuses on finding the domain of functions involving rational expressions. The functions are composed of linear numerators and quadratic denominators, with emphasis on situations where the denominator has real roots. Through a series of questions, learners are asked to identify the correct domain of these functions represented on a number line. This involves determining where the quadratic denominator does not equate to zero to ensure the function's validity across its domain. This skill is crucial for solving problems related to functions in algebra, specifically dealing with domain restrictions and function behavior analysis.

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Function Domain - Fraction Linear over Quadratic (Real Roots) to Number Line

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What number line shows the domain of this function?

f(x)=1x+45x210x15f(x) = \frac{-1x+4}{5x^2-10x-15}

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