Calculus I – Lecture 4: Absolute Value Graphs, Transformations, Equations & Inequalities
Автор: Shadi M. Shaqaqha
Загружено: 2026-02-22
Просмотров: 19
Описание:
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|
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