This math unit starts by introducing synthetic division, focusing on dividing polynomials by binomials and handling remainders. As the unit progresses, it shifts to a detailed study of rational functions, particularly emphasizing the identification and analysis of asymptotes and their influence on function graphs. Students first learn to visually identify different types of asymptotes—including vertical, horizontal, and slant—from rational function graphs. Subsequently, they move on to match asymptotic behaviors to graph presentations and predict these behaviors based on polynomial degrees in numerators and denominators. As the unit deepens, learners explore how to calculate specific types of asymptotes and locate holes in rational functions, either from factored or expanded forms. This portion of the unit enhances their analytical skills in determining function behavior at infinity or undefined points, critical for understanding advanced algebra and calculus concepts. Throughout, the unit interlinks the concepts of function behavior, asymptotic analysis, and polynomial manipulation, culminating in a comprehensive grasp of rational functions and their characteristics.Skills you will learn include:
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