Finding the Equation of a Rational Function Given Two Points

The Organic Chemistry Tutor

This educational video provides a step-by-step tutorial on how to determine the specific equation of a rational function when given its general form and two points that lie on the graph. The video focuses on the rational form y = a/(x-3) + k, demonstrating how to use algebraic substitution to create a system of two linear equations with two variables. It guides viewers through the process of solving this system using the elimination method to find the unknown constants 'a' and 'k'. The content explores key algebraic themes including rational functions, reciprocal functions, asymptotes, and systems of linear equations. It also touches upon function transformations, explaining how the parameters 'a', 'h', and 'k' affect the graph's shape, vertical shifts, and horizontal shifts. The video connects the algebraic solution back to the graphical representation, helping students visualize how the calculated values translate to vertical and horizontal asymptotes. For educators, this video serves as an excellent practical application of solving systems of equations within the context of higher-level function analysis. It is highly useful for Algebra II and Pre-Calculus classrooms to bridge the gap between abstract algebraic manipulation and function modeling. Teachers can use this video to demonstrate why we need as many data points as we have unknown variables and to model best practices for checking mathematical work.