Advanced Functions 12 Study Gu Ide by Paula ThiessenAdvanced Functions 12 Study Gu Ide by Paula Thiessen

Advanced Functions 12 Study Gu Ide

byPaula Thiessen, Laurissa Werhun

Paperback | August 25, 2008

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  • Extends practice and exercises to build skills needed for university bound students
  • Includes key concepts with expanded examples
  • Consumable format which can serve as a reference tool for students as they enter university

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Title:Advanced Functions 12 Study Gu IdeFormat:PaperbackDimensions:10.8 × 8.4 × 0.7 inPublished:August 25, 2008Publisher:McGraw Hill School IndigeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0070724555

ISBN - 13:9780070724556

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Table of Contents

Chapter 1 Polynomial Functions
1.1 Power Functions
   Polynomial Expressions
   Graphs of Power Functions
   Recognize Polynomial Functions
1.2 Characteristics of Polynomial Functions
   Key Features of Graphs of Polynomial Functions
   Relationship Between Finite Differences and the Equation of a Polynomial Function
1.3 Equations and Graphs of Polynomial Functions
   Analyse Graphs of Polynomial Functions
   Analyse Equations to Sketch Graphs of Polynomial Functions
1.4 Transformations
   Roles of a, k, d, and c in Polynomial Functions
   Apply Transformations to Sketch a Graph
   Describe Transformations From an Equation
   Determine an Equation Given the Graph of a Transformed Function
1.5 Slopes of Secants and Average Rate of Change
   Connection Between Average Rate of Change and Slope
   Calculate and Interpret Average Rates of Change From a Graph
   Calculate and Interpret Average Rates of Change From a Table of Values
   Calculate and Interpret Average Rates of Change From an Equation
1.6 Slopes of Tangents and Instantaneous Rate of Change
   Connection Between Slopes of Secants, Slope of a Tangent, and
   Instantaneous Rate of Change
   Estimate Instantaneous Rate of Change From a Graph
   Estimate Instantaneous Rate of Change From a Table of Values
   Estimate Instantaneous Rate of Change From an Equation
Challenge Questions
Chapter 1 Checklist
Chapter 2 Polynomial Equations and Inequalities
2.1 The Remainder Theorem
   Divide a Polynomial by a Binomial
   Apply and Verify the Remainder Theorem
2.2 The Factor Theorem
   Use the Factor Theorem to Find Factors of a Polynomial
   Strategies to Factor a Polynomial
   Combine Factor Theorem and Factoring by Grouping
   Integral Zero Theorem
   Rational Zero Theorem
2.3 Polynomial Equations
   Factoring Polynomial Equations
   Use the Factor Theorem to Solve Polynomial Equations
   Determine the Roots of a Polynomial Equation
2.4 Families of Polynomial Functions
   Represent a Family of Functions Algebraically
   Families of Functions
   Quartic Functions
2.5 Solve Inequalities Using Technology
   Solve Polynomial Inequalities Graphically
   Solve Polynomial Inequalities Numerically
   Solve Problems Involving Inequalities
2.6 Solve Factorable Polynomial Inequalities Algebraically
   Solve Linear Inequalities
   Solve Polynomial Inequalities Algebraically
   Solve Problems using Factorable Polynomial Inequalities
Challenge Questions
Chapter 2 Checklist
Chapter 3 Rational Functions
3.1 Reciprocal of a Linear Function
   Domain, Range, and Asymptotes
   Rate of Change
3.2 Reciprocal of a Quadratic Function
   Domain, Range, and Asymptotes
   Rate of Change
   Key Features of a Function
3.3 Rational Functions of the f(x) = ax + b
                                                   cx + d
   Key Features of Rational Functions of the Form
3.4 Solve Rational Equations and Inequalities f(x) = ax + b
                                                                          cx + d
   Solve Rational Equations Algebraically
   Solve Rational Equations Using Technology
   Solve a Simple Rational Inequality
   Solve a Quadratic Over a Quadratic Rational Inequality
3.5 Making Connections with Rational Functions and Equations
   Solve Problems Using Rational Functions and Equations
Challenge Questions
Chapter 3 Checklist
Chapter 4 Trigonometry
4.1 Radian Measure
   Convert Degree Measure to Radian Measure
   Convert Radian Measure to Degree Measure
   Arc Length for a Given Angle
   Angular Velocity of a Rotating Object
4.2 Trigonometric Ratios and Special Angles
   Apply Trigonometric Ratios for Special Angles
   Trigonometric Ratios for a Multiple of a Special Angle
4.3 Equivalent Trigonometric Expressions
   Use Equivalent Trigonometric Expressions to Evaluate Primary Trigonometric Expressions
   Use an Equivalent Trigonometric Expression to Evaluate a Reciprocal Trigonometric Expression
   Use Technology to Verify Equivalent Trigonometric Expressions
   Trigonometric Identities
4.4 Compound Angle Formulas
   Addition and Subtraction Formulas for Cosine
   Addition and Subtraction Formulas for Sine
   Compound Angle Formulas
4.5 Prove Trigonometric Identities
   Basic Trigonometric Identities
   Provide Formulas and Identities
Challenge Questions
Chapter 4 Checklist
Chapter 5 Trigonometric Functions
5.1 Graphs of Sine, Cosine, and Tangent Functions
   Graphs of the Form y = sin x + c
   Graphs of the Form y = asin x
   Graphs of the Form y = sin(x – d)
   Graphs of the Form y = sink x
5.2 Graphs of Reciprocal Trigonometric Functions
   Determine Values on the Graph of y = csc x
   Determine Values on the Graph of y = cot x
   Reciprocal and Inverse Notation
5.3 Sinusoidal Functions of the Form
   f (x) = a sin [k(x – d)] + c and f (x) = a cos[k(x – d)] + c
   Transform a Cosine Function
   Transform a Sine Function
5.4 Solve Trigonometric Equations
   Solve a Quadratic Trigonometric Equation
   Solve a Quadratic Trigonometric Equation by Factoring
   Solve an Equation Involving Reciprocal Trigonometric Ratios
5.5 Making Connections and Instantaneous Rate of Change
   Average and Instantaneous Rates of Change for a Sinusoidal Function
   Solve Problems Using Instantaneous Rate of Change
Challenge Questions
Chapter 5 Checklist
Chapter 6 Exponential and Logarithmic Functions
6.1 The Exponential Function and Its Inverse
   Features of Exponential Functions
   Write Equations to Fit Data
   Graph Inverse Functions
6.2 Logarithms
   Logarithmic Function
   Write Exponential Equations in Logarithmic Form
   Evaluate Logarithms
   Write Logarithmic Equations in Exponential Form
   Approximate Logarithms
6.3 Transformations of Logarithmic Functions
   Stretches, Reflections, and Translations
6.4 Power Law of Logarithms
   The Power Law of Logarithms
   Solve Problems Using Logarithms
   Evaluate Logarithms
   Graph Logarithmic Functions
6.5 Making Connections: Logarithmic Scales in the Physical Sciences
   Solving Problems Using Logarithmic Scales
Challenge Questions
Chapter 6 Checklist
Chapter 7 Tools and Strategies for Solving Exponential and Logarithmic Equations
7.1 Equivalent Forms of Exponential Equations
   Model Exponential Growth
   Change the Base of Powers
   Solve Equations by Changing the Base
7.2 Techniques for Solving Exponential Equations
   Powers With Different Bases
   Apply the Quadratic Formula
   Extraneous Roots
7.3 Product and Quotient Laws of Logarithms
   Product Law of Logarithms
   Quotient Law of Logarithms
   Simplify Algebraic Expressions
7.4 Techniques for Solving Logarithmic Equations
   Solve Equations Using Logarithms
7.5 Making Connections: Mathematical Modelling With Exponential and Logarithmic Equations
   Select and Apply Mathematical Models
   Solve Problems Using Exponential and Logarithmic Equations
Challenge Questions
Chapter 7 Checklist
Chapter 8 Combining Functions
8.1 Sums and Differences of Functions
   The Superposition Principle
   The Profit Function
8.2 Products and Quotients of Functions
   Solve Problems Using Products and Quotients of Functions
   Combined Functions
8.3 Composite Functions
   Determine Equations for Composite Functions
   Evaluate Composite Functions
8.4 Inequalities of Combined Functions
  Techniques for Illustrating Inequalities
  Solve Inequalities
  Solve Problems Using Inequalities
8.5 Making Connections: Modelling With Combined Functions
  Solve Problems Using Combined Functions
  Develop Models using Combined Functions
Challenge Questions
Chapter 8 Checklist
University Preparation
UP 1 Extending Algebraic Skills
UP 1.1 Factoring Complex Equations
UP 1.2 Techniques for Solving Complex Equations
UP 2 Absolute Value
UP 2.1 Solving Equations Involving Absolute Value
UP 2.2 Solving Inequalities Involving Absolute Value
UP 3 Matrices
UP 3.1 Introduction to Matrices
UP 3.2 Determinants
UP 4 Conics
UP 4.1 Introduction
UP 4.2 The Elipse
UP 4.3 The Hyperbola
Practice Exam