Mastering Graphs of Exponential and Logarithmic Functions

Miacademy & MiaPrep Learning Channel

This comprehensive math tutorial explores the graphical relationship between exponential and logarithmic functions, explicitly connecting them as inverse functions. Through clear visualizations, the video demonstrates how the input and output values of base-2 exponential functions are swapped to create logarithmic functions, resulting in a reflection over the line y=x. It breaks down the key features of both function types, including domain, range, intercepts, and asymptotic behavior, for both growth and decay scenarios. The content progresses from fundamental concepts to more advanced applications involving transformations. It provides a detailed review of how parameters affect the parent functions, covering vertical and horizontal stretches, compressions, reflections, and translations. The narrator emphasizes the importance of the order of operations when applying these transformations—performing scalings and reflections before translations. Ideal for Algebra II and Precalculus classrooms, this video offers significant educational value by bridging abstract algebraic concepts with concrete visual representations. It includes two step-by-step worked examples that challenge students to identify transformations, determine asymptotes, calculate intercepts, and sketch graphs of complex functions. The inclusion of pause points for student practice makes it a ready-to-use resource for interactive learning.