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Student and Tutor practiced analyzing rational functions, including identifying horizontal and vertical asymptotes, x- and y-intercepts, and potential holes through factorization and synthetic division. They also reviewed the discriminant method for solving quadratic equations to find x-intercepts when direct factorization is not possible. The plan for the next session includes creating short notes and working on questions from test sections 4.1 and 4.2.

The Student and Tutor engaged in a comprehensive session on rational functions. They practiced identifying horizontal and vertical asymptotes, x and y-intercepts, and holes, including a detailed discussion on factoring higher-degree polynomials using synthetic division. The session concluded with a homework assignment for the Student to graph a complex rational function.

The Tutor and Student started with a review of synthetic division and factoring. They then revised horizontal asymptotes for rational functions, defined x and y-intercepts, and introduced vertical asymptotes. The session heavily focused on applying these concepts to two complex rational functions, including calculating all asymptotes and intercepts, and determining the function's graphical behavior around vertical asymptotes using sign analysis. They planned to continue practicing these types of questions due to their importance for exams.

The Student and Tutor reviewed the process of synthetic division for factoring polynomials and finding roots, practicing with several examples. They then introduced rational functions and focused extensively on determining horizontal asymptotes using three specific rules based on the degrees of the polynomials. The next session will cover vertical asymptotes and graph plotting.

The Student and Tutor reviewed various applied mathematics and economics problems, including population growth models, tax revenue maximization using calculus, and concepts related to production functions and demand elasticity. They worked through specific calculations and problem-solving steps to prepare for an upcoming exam, with the Tutor emphasizing careful differentiation and formula application.

The Tutor and Student practiced modeling functions by solving word problems involving geometric shapes like rectangles, boxes, and cylinders. They focused on expressing area and volume in terms of a single variable, reviewing key formulas for perimeter, area, and volume. For homework, the Student was asked to review the current chapter's concepts and prepare for the next chapter on rational functions by attempting random questions.