Transformations of Functions | Shifts, Stretches, Reflections Explained скачать в хорошем качестве

Transformations of Functions | Shifts, Stretches, Reflections Explained

📚 Master Transformations of Functions with Clear Visual Examples! Transformations allow you to shift, stretch, compress, and reflect graphs of functions. In this video, you’ll learn how each type of transformation affects the graph of a function, and how to write equations that represent these changes. We cover: ✔ Vertical and horizontal shifts (translations) ✔ Vertical and horizontal stretches and compressions (scaling) ✔ Vertical and horizontal reflections By the end of this lesson, you’ll be able to identify and apply each type of transformation with confidence! 🔍 What You’ll Learn in This Video: ✅ 1. Translations – Shifting Graphs: ✔ Vertical shifts:  • f(x) + c shifts up  • f(x) - c shifts down ✔ Horizontal shifts:  • f(x + c) shifts left  • f(x - c) shifts right ✅ 2. Scaling – Stretching and Compressing Graphs: ✔ Vertical Stretch/Compression:  • c·f(x) stretches vertically by factor c  • f(x)/c compresses vertically by factor c ✔ Horizontal Stretch/Compression:  • f(cx) compresses horizontally by factor c  • f(x/c) stretches horizontally by factor c ✅ 3. Reflections – Flipping Graphs: ✔ Vertical reflection: -f(x) flips graph over the x-axis ✔ Horizontal reflection: f(-x) flips graph over the y-axis ✅ Example Problems: ✔ Use basic functions like f(x) = x or f(x) = x² to explore transformations ✔ Identify equations based on transformations shown on graphs ✔ Combine multiple transformations into a single expression ✅ Common Mistakes to Avoid: ✔ Confusing horizontal vs. vertical shifts ✔ Reversing the effect of reflections or stretches ✔ Forgetting to apply transformations in the correct order By the end of this video, you’ll know how to transform any function and predict its graph—a key skill in algebra, precalculus, and calculus! 📥 Download Free Guided Notes! Get guided notes to follow along and practice transformations step by step: 👉 https://www.understandthemath.com/alg... 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Connect & Support Support: https://buymeacoffee.com/understandth... Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Pinterest: https://pin.it/2YAWfM2zP Timestamps 00:00 Introduction 00:23 Translation - Vertical Shifts 03:35 Translation - Horizontal Shifts 07:17 Scaling - Vertical Stretching and Compressing 11:21 Scaling - Horizontal Stretching and Compressing 16:37 Reflecting - Vertical and Horizontal More About Understand The Math Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples. Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective. #FunctionTransformations #MathHelp #Algebra #Precalculus #LearnMath #StudyMath #GraphingFunctions #TransformingFunctions #MathTutorial #UnderstandTheMath #HighSchoolMath #MathMadeEasy #ShiftingGraphs #StretchingGraphs #Reflections