Скачать или смотреть 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|