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# Advanced Functions 12: Study Guide And University Handbook

## byLaurissa Werhun, Paula Thiessen

### Paperback | August 25, 2008

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### about

- 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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The following ISBNs are associated with this title:

ISBN - 10:0070724555

ISBN - 13:9780070724556

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Table of Contents

**Overview**

Formulas** ****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

Symmetry

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

Intercepts

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

Translations

Stretches, Reflections, and Translations

Transformations

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

Half-Life

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

Answers