How to Graph Functions Using Input-Output Tables

Mashup Math

This instructional video provides a clear, step-by-step tutorial on how to graph a cubic function by creating and filling out an input-output table. The narrator demystifies the notation of functions by encouraging viewers to think of 'x' simply as a placeholder for an input value, demonstrating this visually by replacing 'x' with an orange circle. The video walks through the specific example of f(x) = x^3 - 6x, evaluating the function for various integer inputs to generate coordinate points. The content covers key algebraic skills including substitution, operations with exponents, handling negative numbers, and plotting points on a Cartesian coordinate plane. It transitions from algebraic calculation to geometric visualization as the calculated points are plotted and connected with a smooth curve. The narrator emphasizes the specific shape of cubic functions, noting the characteristic "peak and valley" curve, distinguishing it from linear or quadratic graphs. For educators, this video serves as an excellent introduction or review of graphing functions without a graphing calculator. It reinforces the fundamental concept that a graph is simply a visual representation of many input-output pairs. The visual aids, specifically the color-coded substitution and the animation of points appearing on the graph, make abstract algebraic concepts concrete and accessible for students in Pre-Algebra and Algebra I.