This math unit begins by exploring the end behavior of polynomial functions, teaching students how to analyze and predict the behavior of polynomials as \(x\) approaches infinity or negative infinity based on their degrees and leading coefficients. Initially, students learn to match descriptions of end behaviors with corresponding polynomial functions, and then progress to applying rules related to the powers and coefficients for determining the direction of the graph's tails at extremes. The unit then shifts focus to the root behavior of polynomials, examining how graphs can illustrate the behavior at various roots, and how functions can be analyzed to determine roots and their multiplicities. Students also work with translating between the graphical representation of polynomials and their equation forms, including determining the behavior based on intercepts and vice versa. Lastly, the unit covers the calculation of the average rate of change of functions, where students learn to compute slopes from graphs and algebraic functions, linking it to practical scenarios such as rate of change in real-world phenomena. This passage through the unit provides a comprehensive understanding of polynomial behaviors and derivative concepts through varied representations and increasing complexity in application.Skills you will learn include:
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