Section 2.2 the graph of a function
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The document discusses graphs of functions and examples of functions and non-functions. It provides examples of equations and their classifications as functions or not functions. It also includes copyright information for Pearson Education as the publisher.
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Pat05 ppt 0201
This document provides an overview of functions and concepts covered in Chapter 2, including:
- Graphing functions to identify intervals where they are increasing, decreasing, or constant.
- Modeling real-world applications with appropriate functions.
- Graphing functions defined piecewise using different formulas for different parts of the domain.
- Identifying relative maximum and minimum values of functions.
- Defining functions as increasing, decreasing, or constant on intervals.
- Describing the greatest integer function.
Section 5.5 properties of logarithms
This document contains examples of properties of logarithms, including:
1) Writing logarithms with the same base as a sum or difference of logarithms by using properties 1-4
2) Expressing logarithms with different bases in terms of a single logarithm using properties 5-6
3) Approximating logarithms by changing them to an exponential form and using properties 5 and 7
The document provides step-by-step workings for each example and identifies the relevant property of logarithms used at each step.
Taylor introms10 ppt_02
This document provides an overview of linear programming models, including how to formulate optimization models, graphical solutions, and irregular model types. It begins with the objectives and steps of linear programming. Key sections describe how to set up maximization and minimization models with examples, representing constraints graphically, and handling multiple optimal solutions, infeasible solutions, and unbounded models. The document uses examples to demonstrate each component of linear programming model formulation and solution.
Pat05 ppt 0105
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- Derivatives of logarithmic and exponential functions
- Elasticity of demand
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- Logarithmic differentiation
- Newton's method for approximating roots
- Finding higher-order derivatives directly and implicitly.
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Introductory maths analysis chapter 12 official
This chapter discusses additional topics in differentiation including:
- Derivatives of logarithmic and exponential functions
- Elasticity of demand
- Implicit differentiation
- Logarithmic differentiation
- Newton's method for approximating roots
- Finding higher-order derivatives directly and implicitly.
Examples are provided for each topic to illustrate the differentiation techniques.
Chapter12 additionaldifferentiationtopics-151003154510-lva1-app6891
This chapter discusses additional topics in differentiation including:
- Derivatives of logarithmic and exponential functions
- Elasticity of demand
- Implicit differentiation
- Logarithmic differentiation
- Newton's method for approximating roots
- Finding higher-order derivatives directly and implicitly.
Examples are provided for each topic to illustrate the differentiation techniques.
end behavior.....pptx
This document discusses polynomial functions and how to graph them. It begins by listing the objectives of understanding the definition of a polynomial function, sketching power functions, determining end behavior, intercepts, real zeros and their multiplicities, and sketching the graph. It then defines polynomial functions and provides examples of determining if a function is polynomial. It also discusses how to sketch power functions, determine end behavior, find intercepts, real zeros and their multiplicities, and use a four step process to sketch the graph of a polynomial function.
Introductory maths analysis chapter 02 official
The document discusses functions and graphs in chapter 2 of an introductory mathematical analysis textbook. It introduces key concepts such as functions, domains, ranges, combinations of functions, inverse functions, and graphs in rectangular coordinates. It provides examples of determining equality of functions, finding function values, combining functions, and finding inverses. It also discusses special functions, graphs, symmetry, and intercepts. The chapter aims to define functions and domains, introduce different types of functions and their operations, and familiarize students with graphing equations and basic function shapes.
Chapter2 functionsandgraphs-151003144959-lva1-app6891
This chapter discusses functions and graphs. It introduces different types of functions including constant, special, rational, and absolute value functions. It covers combining functions using addition, subtraction, multiplication, and composition. Inverse functions and their properties are explained. Graphing functions in a rectangular coordinate system and finding intercepts is demonstrated. The chapter also discusses symmetry of graphs about the x-axis, y-axis, origin, and line y = x.
Chapter 2 - Functions and Graphs
This chapter discusses functions and graphs. It introduces different types of functions including constant, special, rational, and absolute value functions. It covers combining functions using addition, subtraction, multiplication, and composition. Inverse functions and their properties are explained. Graphing functions in a rectangular coordinate system and finding intercepts is demonstrated. The chapter also discusses symmetry of graphs about the x-axis, y-axis, origin, and line y = x.
Section 5.3 exponential functions
The document is a copyright notice repeated multiple times. It states that the content is copyrighted by Pearson Education, Inc. in 2012 for their Prentice Hall publishing brand. No other substantive information is provided.
Section 5.3 exponential functions
The document is a copyright notice repeated multiple times. It states that the content is copyrighted by Pearson Education, Inc. in 2012 for their Prentice Hall publishing brand. No other substantive information is provided.
Pat05 ppt 0106
This document discusses solving linear inequalities and compound inequalities. It provides examples of solving various inequalities algebraically and graphing their solution sets. It also gives an example of setting up and solving an inequality to model a real-world situation about payment plans for a house painting job.
Introductory maths analysis chapter 00 official
This document is the introduction to a textbook on introductory mathematical analysis. It provides an overview of the chapters included in the textbook, which cover topics such as algebra, functions, calculus, probability, and multivariable calculus. Chapter 0 provides a review of key concepts in algebra, including sets of real numbers, properties of real numbers, exponents and radicals, algebraic expressions, factoring, fractions, and solving different types of equations. The chapter objectives and outlines are presented for Chapter 0.
Chapter0 reviewofalgebra-151003150137-lva1-app6891
This document is the introduction to a textbook on introductory mathematical analysis. It provides an overview of the chapters included in the textbook, which cover topics such as algebra, functions, calculus, probability, and multivariable calculus. Chapter 0 provides a review of key concepts in algebra, including sets of real numbers, properties of real numbers, exponents and radicals, algebraic expressions, factoring, fractions, and solving equations. The chapter objectives are to review these algebraic topics and refresh the reader's knowledge before advancing to subsequent mathematical concepts.
Similar to Section 2.2 the graph of a function (20)
Lecture 5 sections 2.1-2.2 coordinate plane and graphs-
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Chapter12 additionaldifferentiationtopics-151003154510-lva1-app6891
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Section 2.2 the graph of a function
- 1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 2.2 The Graph of a Function
- 2. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 3. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 4. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Which of the following are graphs of functions? A Function A Function
- 5. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Which of the following are graphs of functions? Not A Function Not A Function
- 6. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 7. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( )(a) 0 4f = { } [ ](b) 0 4 or 0,4x x π π≤ ≤ { } [ ](c) 4 4 or 4,4y y− ≤ ≤ − Four times.
- 8. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( )Consider the function 1 x f x x = + ( ) 2 2 2 2 1 3 f = = + Yes 2 2, 3 ÷ ( ) 1 1 1 1 21 f = = + ( ) 2 1 xf x x = = + ( )2 1x x+ = 2 2x x+ = 2x = − ( )2,2−
- 9. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 10. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.