Calculus I – Lecture 4: Absolute Value Graphs, Transformations, Equations & Inequalities скачать в хорошем качестве

Calculus I – Lecture 4: Absolute Value Graphs, Transformations, Equations & Inequalities

In this lecture, we study the absolute value function and its geometric meaning as distance on the real line. Topics covered: Definition and properties of the absolute value Piecewise representation Graph of 𝑦=∣𝑥∣ Graph transformations Solving absolute value equations Solving absolute value inequalities Rational inequalities involving absolute value Emphasis is placed on graphical interpretation and sign analysis. Students are encouraged to write along and pause the video when needed. Instructor: Prof. Shadi Shaqaqha Department of Mathematics – Yarmouk University شرح شامل لدالة القيمة المطلقة وتحويلاتها وحل المعادلات والمتباينات المرتبطة بها. 00:00 Definition of Absolute Value & Properties 03:10 Rewriting |3x² − 6| as Piecewise Function 06:50 Graph Interpretation & Reflection About x-axis 08:02 Graph of y = |x| and Transformations 10:39 Examples of Graph Transformations 13:54 Solving Absolute Value Equations 15:35 Solving Absolute Value Inequalities 18:25 Rational Inequality with Absolute Value 21:32 Alternative Solution Using |x|