Engineer turned to educator equipped with strong fundamental and complex problem solving abilities. Let's get the learning started.

Student and Tutor primarily focused on functions, specifically inverse functions, domain and range restrictions, and the composition of functions. They practiced solving problems involving transformations of functions and identifying inverse relationships, with a particular emphasis on determining valid domains for root functions in preparation for an upcoming exam.

The Student and Tutor practiced finding inverse functions for various algebraic expressions, including quadratic, rational, and polynomial types. They also focused extensively on determining the domain and range for both original and inverse functions, paying close attention to conditions that render a function unsolvable. Additionally, they worked on interpreting function and inverse function values from graphs and plotting inverse functions.

The Tutor and Student extensively covered functions, starting with matching graphs to various function types. They practiced graph transformations, including reflections across axes and the origin, and translations. A significant portion of the class focused on inverse functions, including their algebraic calculation, evaluation, verification through composition, and interpretation from tables, with domain and range deferred to the next session.

Student and Tutor thoroughly reviewed function transformations, covering graphing root functions, identifying parent functions from given equations, and distinguishing between reflections, stretches, and various shifts. They practiced writing equations for transformed graphs, including parabolas and rational functions, and concluded by solving a complex problem integrating multiple transformation types. The Student will complete the remaining worksheet for homework.

The Student and Tutor worked on graphing various functions, including square root and quadratic functions, by plotting specific points. They then focused on understanding function transformations, such as vertical and horizontal shifts, vertical stretching, and reflections. The Student will need to review these concepts as the chapter felt comprehensive.

The Student and Tutor reviewed key concepts in functions, including evaluation of functions, the definition of differentiation, and calculating the domain of various function types (linear, rational, and radical). They also practiced composing and evaluating nested functions. The Student mentioned an upcoming exam.