This math unit covers essential aspects of function transformations, starting from understanding how simple transformations affect the vertex of a function, to more complex manipulations that alter the domain and range. It begins by teaching students how to identify and apply transformations like shifts and reflections that lead to changes in the vertex of functions. The unit progresses to more intricate transformations affecting the domain and range, requiring students to reverse-engineer transformations from changes in these properties. The unit further expands into function composition, focusing on determining and representing the domain of composite functions, which is complemented by ensuring understanding of conditions around real roots in quadratic functions nested within other functions. Additionally, the course transitions into determining inverses specifically between exponential and logarithmic functions, and thoroughly explores sinusoidal functions where students progressively learn to identify and relate parameters like amplitude, phase shifts, and vertical shifts from both algebraic forms and their corresponding graphs. This comprehensive approach not only strengthens algebraic manipulation skills but also enhances visual and theoretical understanding of various function transformations and their applications in greater math contexts.Skills you will learn include:
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