This math unit focuses on progressively developing students' understanding and skills in identifying the domain of various functions, beginning with simpler quadratic functions and moving toward more complex rational functions involving polynomials, square roots, and complex roots. Initially, students learn to determine and visually represent the domain of quadratic functions on a number line. They then explore polynomial functions of higher powers, followed by functions involving square roots of linear and quadratic expressions, requiring careful analysis of conditions that ensure real number outputs. The unit advances into exploring the domain of functions where integers and linear expressions are in the numerator, and quadratic expressions, including those with complex roots, are in the denominator. Further complexities involve understanding and representing domains of functions combining square roots and quadratic components in both the numerator and the denominator, culminating in an analysis of conditions that maintain function validity, particularly focusing on real numbers and avoiding undefined behaviors like division by zero.Skills you will learn include:
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