Precálculo - 6 Desplazamiento de gráficas

🔄 Function Transformations: Horizontal and Vertical Shifts | Precalculus Did you know that moving a graph in the plane is as simple as changing x to x−h or y to y−k? In this video, we explore horizontal and vertical shifts of functions, showing how small substitutions in their equations generate precise shifts in their graph, just as we saw earlier with shifted conics. 🎯 In this video you will learn: Horizontal shift: f(x)→f(x−h): shifts the graph h units to the right if h is positive Vertical shift: f(x)→f(x)+k: shifts the graph k units upward if k is positive The connection to conics: Example: from x^2+y^2=r^2 (center at origin) to (x−h)^2+(y−k)^2=r^2 (center at (h,k)) Animations in GeoGebra: Observe how the graph moves as h and k vary in real time Examples with functions 📐 Applications: These transformations are essential in computer animation, graphic design, physics (trajectory motion), and model optimization. 👨‍🏫 Visual and intuitive approach: Step-by-step explanations, use of GeoGebra to visualize displacements, and connections to previous topics. Ideal for high school students. 🔔 Did you like the video? Subscribe and activate the bell 🔔 so you don't miss the next videos where we'll explore more transformations. Move graphs like an expert! #FunctionTransformations #Displacements #GeoGebra #Precalculus #VisualMath #LearnMath #HigherSecondaryEducation