Calculus 1 Lecture 2 PDF
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This document is a lecture on Calculus 1, focusing on various types of functions, their representations, and transformations presented through graphs and formulas. It includes examples and related problems.
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Calculus 1 Lec.2 D R. D O A A E Z Z AT DR. ESRAA ABDELRAOUF DR. DALIA SHOMAN Chapter 1 Functions (1.2) Representing Functions Representing Functions 1. Words: The least mathematical way to define functions. 2. Table: contains some data obtained from certain experiments....
Calculus 1 Lec.2 D R. D O A A E Z Z AT DR. ESRAA ABDELRAOUF DR. DALIA SHOMAN Chapter 1 Functions (1.2) Representing Functions Representing Functions 1. Words: The least mathematical way to define functions. 2. Table: contains some data obtained from certain experiments. 3. Graph: provides the most illuminating representations. 4. Formula: the most compact way to represent many functions. Representing Functions using Tables Representing Functions using Graphs 1. Linear Functions 2. Piecewise Functions 3. Power and Root Functions 4. Rational Functions 1. Linear Functions 1. Linear Functions (Example) 1. Linear Functions (Example) 2. Piecewise Functions Piecewise Functions: A function may have different definitions on different parts of its domain. For example, income tax is levied in tax brackets that have different tax rates. Functions that have different definitions on different parts of their domain are called piecewise functions. If all the pieces are linear, the function is piecewise linear. 2. Piecewise Functions (Example) 3. Power and Root Functions 3. Power and Root Functions: Power Functions (n is even) 3. Power and Root Functions: Power Functions (n is odd) 3. Power and Root Functions 3. Power and Root Functions : Root Functions (n is even) 3. Power and Root Functions: Root Functions (n is odd) Representing functions using Formulas Representing functions using Formulas (Cont.) Representing functions using Formulas Composite Functions Composite Functions Domain of Composite Functions Example Example Another Example Another Example Important Example on Composite Functions Important Example on Composite Functions Graph Transformation Vertical Shift Horizontal Shift Vertical Scale Vertical Scale with Reflection across the x-axis Horizontal Scale Horizontal Scale with Reflection across the y-axis Example Link of Lectures & Book https://drive.google.com/drive/folders/12eHtoXkLoQ RJSeyAcAFMgiZ-jps7trWq?usp=sharing Thank you
