This math unit focuses on the mastery of function transformations and their applications across various types of functions. Starting with basic vertex transformations of quadratic functions, students learn to manipulate and understand how single and double transformations affect the vertex's position. As the unit progresses, these concepts are extended to examining how transformations influence the domain and range of functions, reinforcing the understanding of function behavior under algebraic manipulations. In the latter half of the unit, students delve into function composition and its impact on domain specifications, tackling more complex scenarios like rational functions composed with linear functions and determining their viable input values. The unit culminates with a detailed study of sinusoidal functions, where students analyze and derive function equations from given graphs and vice versa, learning to identify key function parameters such as amplitude, period, and phase shifts. Throughout the unit, they progressively build from basic transformation concepts to applying these in varied contexts, including exponential, logarithmic, and trigonometric functions, enhancing their overall comprehension and capability in function analysis and application.Skills you will learn include:
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