# Functions and Applications 11 McGraw-Hill Ryerson PDF: A Comprehensive Guide for Math Students

## Functions and Applications 11 McGraw-Hill Ryerson PDF

Are you looking for a comprehensive and engaging math textbook that covers the Ontario curriculum for Grade 11 University/College Preparation (MCF3M)? Do you want to have access to a digital version of the textbook that you can read on your computer, tablet, or smartphone? If so, you might be interested in Functions and Applications 11 McGraw-Hill Ryerson PDF.

## functionsandapplications11mcgrawhillryersonpdf13

## Introduction

In this article, we will give you an overview of what Functions and Applications 11 is, why it is important to learn math, and how you can access the PDF version of the textbook. We will also provide you with brief summaries of each chapter, highlighting the key concepts and sample problems that you will encounter. By the end of this article, you will have a better understanding of what Functions and Applications 11 has to offer and how you can use it to improve your math skills.

### What is Functions and Applications 11?

Functions and Applications 11 is a math textbook that follows the Ontario curriculum for Grade 11 University/College Preparation (MCF3M). It is published by McGraw-Hill Ryerson, a leading educational publisher in Canada. The textbook covers topics such as quadratic relations, exponential functions, trigonometric functions, discrete functions, and financial applications. It also includes features such as:

Real-world examples and applications that connect math to everyday life

Practice questions and exercises that reinforce learning and develop problem-solving skills

Technology tips that show how to use graphing calculators and software to explore math concepts

Review sections that summarize key ideas and provide extra practice

Self-assessment tools that help students monitor their progress and identify areas for improvement

Online resources that provide additional support and enrichment opportunities

### Why is it important to learn math?

Math is not only a subject that you have to study in school, but also a skill that you need in life. Math helps you develop logical thinking, critical thinking, creativity, and communication skills. Math also enables you to understand and appreciate the patterns and structures of nature, science, art, music, and more. Math also prepares you for various careers and fields of study that require mathematical knowledge and reasoning. Some examples are:

Engineering

Computer science

Business

Medicine

Economics

Psychology

Education

Social sciences

And many more!

### How can you access the PDF version of the textbook?

If you are enrolled in a course that uses Functions and Applications 11 as the textbook, you can access the PDF version of the textbook for free through your teacher or school. You will need a username and password to log in to the McGraw-Hill Ryerson website. Once you are logged in, you can download or view the PDF version of the textbook on your device. You can also print out pages or sections of the textbook if you prefer.

If you are not enrolled in a course that uses Functions and Applications 11 as the textbook, but you still want to access the PDF version of the textbook, you can purchase it online from the McGraw-Hill Ryerson website. You will need to create an account and pay a fee to download or view the PDF version of the textbook. The fee varies depending on whether you want to access the textbook for one year or for four years.

## Chapter Summaries

In this section, we will give you a brief overview of each chapter in Functions and Applications 11. We will highlight the key concepts and sample problems that you will encounter in each chapter. We will also provide you with a table that shows the learning goals and expectations for each chapter.

### Chapter 1: Working with Quadratic Relations

#### Key Concepts

In this chapter, you will learn how to:

Determine whether a relation is linear or quadratic by examining its table of values, graph, or equation

Identify the vertex, axis of symmetry, zeros, y-intercept, domain, and range of a quadratic relation

Solve quadratic equations by factoring, completing the square, or using the quadratic formula

Analyze real-world situations involving quadratic relations such as projectile motion, area optimization, revenue maximization, etc.

#### Sample Problems

Here are some sample problems from this chapter:

Determine whether each relation is linear or quadratic. Explain your reasoning.

x-2-1012

y-6-20-2-6

The graph of y = ax^2 + bx + c has a vertex at (2,-5) and passes through (0,-1). Determine the values of a, b, and c.

Solve x^2 - 5x - 24 = 0 by factoring.

A soccer ball is kicked into the air from ground level with an initial velocity of 25 m/s at an angle of 45 with respect to the horizontal. The height h (in metres) of the ball above the ground after t seconds is given by h = -5t^2 + 25t2. a) What is the maximum height reached by the ball? b) How long does it take for the ball to hit the ground?

Chapter 1: Working with Quadratic Relations

Learning Goals and Expectations

Demonstrate an understanding of...Demonstrate an ability to...

The characteristics of quadratic relations (e.g., vertex form equation; vertex; axis of symmetry; zeros; y-intercept; domain; range)Determine whether a relation is linear or quadratic by examining its table of values, graph, or equation Identify the characteristics of a quadratic relation from its table of values, graph, or equation Sketch the graph of a quadratic relation given its table of values, equation, or characteristics Solve quadratic equations by factoring, completing the square, or using the quadratic formula Analyze real-world situations involving quadratic relations (e.g., projectile motion; area optimization; revenue maximization)

Assessment Focus: Knowledge/Understanding; Thinking/Inquiry; Communication; Application

Assessment Methods: Quizzes; Tests; Assignments; Projects; Presentations

Assessment Criteria: Accuracy; Completeness; Clarity; Relevance

Assessment Tools: Rubrics; Checklists; Answer Keys

Assessment Feedback: Descriptive Feedback; Peer Feedback; Self-Assessment

Assessment Accommodations: Extra Time; Oral Responses; Scribe Services

Assessment Resources: Textbook; Calculator; Software; Internet

### Chapter 2: Characteristics of Quadratic Relations

#### Key Concepts

In this chapter, you will learn how to:

Identify the transformations of a quadratic relation given its equation in vertex form or standard form

Write the equation of a quadratic relation given its graph or characteristics

Compare and contrast different forms of quadratic equations (i.e., vertex form, standard form, and factored form)

Use the discriminant to determine the number and nature of the zeros of a quadratic relation

Graph quadratic inequalities and solve systems of linear-quadratic equations graphically and algebraically

#### Sample Problems

Here are some sample problems from this chapter:

Describe the transformations of y = -2(x + 3)^2 + 5 compared to y = x^2.

Write the equation of the quadratic relation whose graph has a vertex at (-2,3) and passes through (0,-1).

What are the advantages and disadvantages of using vertex form, standard form, and factored form to represent quadratic relations?

Determine the number and nature of the zeros of y = x^2 - 4x - 5 using the discriminant.

Graph y > x^2 - 2x - 3 and shade the region that represents the solution.

Chapter 2: Characteristics of Quadratic Relations

Learning Goals and Expectations

Demonstrate an understanding of...Demonstrate an ability to...

The transformations of quadratic relations (e.g., translations; reflections; stretches; compressions)Identify the transformations of a quadratic relation given its equation in vertex form or standard form Write the equation of a quadratic relation given its graph or characteristics Compare and contrast different forms of quadratic equations (i.e., vertex form; standard form; factored form) Use the discriminant to determine the number and nature of the zeros of a quadratic relation Graph quadratic inequalities and solve systems of linear-quadratic equations graphically and algebraically

Assessment Focus: Knowledge/Understanding; Thinking/Inquiry; Communication; Application

Assessment Methods: Quizzes; Tests; Assignments; Projects; Presentations

Assessment Criteria: Accuracy; Completeness; Clarity; Relevance

Assessment Tools: Rubrics; Checklists; Answer Keys

Assessment Feedback: Descriptive Feedback; Peer Feedback; Self-Assessment

Assessment Accommodations: Extra Time; Oral Responses; Scribe Services

Assessment Resources: Textbook; Calculator; Software; Internet

### Chapter 3: Exponential Functions

#### Key Concepts

In this chapter, you will learn how to:

Recognize and describe exponential growth and decay patterns in various contexts (e.g., population growth; radioactive decay; compound interest; pH scale)

Identify the characteristics of exponential functions (e.g., asymptote; y-intercept; domain; range; growth or decay factor; growth or decay rate)

Graph exponential functions using transformations of the parent function y = b^x

Solve exponential equations using common bases, logarithms, or graphing technology

Use exponential functions to model and analyze real-world situations (e.g., bacterial growth; carbon dating; half-life; pH level)

#### Sample Problems

Here are some sample problems from this chapter:

The population of a town is 5000 and increases by 2% each year. Write an exponential function to model the population growth. What will the population be in 10 years?

The graph of y = 2^x is transformed to y = -3(2)^(-x + 1) - 2. Describe the transformations and sketch the graph.

Solve 5^(2x - 1) = 125 using common bases.

A radioactive substance has a half-life of 12 hours. How much of a 100 g sample will remain after 36 hours?

The pH of a solution is defined as pH = -log[H+], where [H+] is the concentration of hydrogen ions in moles per litre. What is the pH of a solution with [H+] = 0.0001?

Chapter 3: Exponential Functions

Learning Goals and Expectations

Demonstrate an understanding of...Demonstrate an ability to...

The characteristics of exponential functions (e.g., asymptote; y-intercept; domain; range; growth or decay factor; growth or decay rate)Recognize and describe exponential growth and decay patterns in various contexts (e.g., population growth; radioactive decay; compound interest; pH scale) Identify the characteristics of an exponential function given its table of values, graph, or equation Graph exponential functions using transformations of the parent function y = b^x Solve exponential equations using common bases, logarithms, or graphing technology Use exponential functions to model and analyze real-world situations (e.g., bacterial growth; carbon dating; half-life; pH level)

Assessment Focus: Knowledge/Understanding; Thinking/Inquiry; Communication; Application

Assessment Methods: Quizzes; Tests; Assignments; Projects; Presentations

Assessment Criteria: Accuracy; Completeness; Clarity; Relevance

Assessment Tools: Rubrics; Checklists; Answer Keys

Assessment Feedback: Descriptive Feedback; Peer Feedback; Self-Assessment

Assessment Accommodations: Extra Time; Oral Responses; Scribe Services

Assessment Resources: Textbook; Calculator; Software; Internet

### Chapter 4: Trigonometric Functions

#### Key Concepts

In this chapter, you will learn how to:

Review the primary trigonometric ratios (sine, cosine, and tangent) and the reciprocal trigonometric ratios (cosecant, secant, and cotangent)

Use the Pythagorean theorem, the sine law, and the cosine law to solve problems involving right and non-right triangles

Define and graph the trigonometric functions y = sin x, y = cos x, and y = tan x using the unit circle

Identify the characteristics of trigonometric functions (e.g., amplitude; period; phase shift; vertical shift; domain; range)

Graph transformations of trigonometric functions using the general equation y = a sin [b(x - c)] + d or y = a cos [b(x - c)] + d

Solve trigonometric equations using algebraic methods or graphing technology

Use trigonometric functions to model and analyze periodic phenomena (e.g., sound waves; tides; Ferris wheel)

#### Sample Problems

Here are some sample problems from this chapter:

In triangle ABC, angle A is 35, angle B is 90, and side b is 12 cm. Find the length of side c.

What are the exact values of sin 60, cos 60, and tan 60 using the unit circle?

The graph of y = sin x is transformed to y = -2 sin (3x + Ï€) - 1. Describe the transformations and sketch the graph.

Solve 2 sin x - 1 = 0 for 0 x < 2Ï€.

The height h (in metres) of a person on a Ferris wheel after t minutes is given by h = 10 sin (0.5Ï€t) + 12. What is the maximum height reached by the person? How long does it take for one complete rotation?

Chapter 4: Trigonometric Functions

Learning Goals and Expectations

Demonstrate an understanding of...Demonstrate an ability to...

The characteristics of trigonometric functions (e.g., amplitude; period; phase shift; vertical shift; domain; range)Review the primary trigonometric ratios (sine, cosine, and tangent) and the reciprocal trigonometric ratios (cosecant, secant, and cotangent) Use the Pythagorean theorem, the sine law, and the cosine law to solve problems involving right and non-right triangles Define and graph the trigonometric functions y = sin x, y = cos x, and y = tan x using the unit circle Identify the characteristics of a trigonometric function given its table of values, graph, or equation Graph transformations of trigonometric functions using the general equation y = a sin [b(x - c)] + d or y = a cos [b(x - c)] + d Solve trigonometric equations using algebraic methods or graphing technology Use trigonometric functions to model and analyze periodic phenomena (e.g., sound waves; tides; Ferris wheel)

Assessment Focus: Knowledge/Understanding; Thinking/Inquiry; Communication; Application

Assessment Methods: Quizzes; Tests; Assignments; Projects; Presentations

Assessment Criteria: Accuracy; Completeness; Clarity; Relevance

Assessment Tools: Rubrics; Checklists; Answer Keys

Assessment Feedback: Descriptive Feedback; Peer Feedback; Self-Assessment

Assessment Accommodations: Extra Time; Oral Responses; Scribe Services

Assessment Resources: Textbook; Calculator; Software; Internet

### Chapter 5: Discrete Functions

#### Key Concepts

In this chapter, you will learn how to:

Distinguish between discrete and continuous functions by examining their domains and graphs

Recognize and describe arithmetic and geometric sequences and series using recursive and explicit formulas

Calculate the nth term, the partial sum, and the infinite sum of arithmetic and geometric sequences and series

Use sigma notation to represent arithmetic and geometric series

Use discrete functions to model and analyze real-world situations (e.g., population growth; compound interest; annuities; mortgages)

#### Sample Problems

Here are some sample problems from this chapter:

Which of the following functions are discrete and which are continuous? Explain your reasoning. a) y = 2x + 3 b) y = x^2 - 5 c) y = floor(x), where floor(x) is the greatest integer less than or equal to x d) y = 3^x

Write a recursive formula and an explicit formula for each sequence. Identify whether the sequence is arithmetic or geometric. a) 2, 5, 8, 11, ... b) 1, 2, 4, 8, ...

Find the 10th term, the sum of the first 10 terms, and the sum to infinity (if it exists) of each series. a) 3 + 6 + 9 + 12 + ... b) 1 + 1/2 + 1/4 + 1/8 + ...

Write each series using sigma notation. a) 5 + 10 + 15 + ... + 50 b) 1/2 + 1/4 + 1/8 + ... + 1/1024

A car loan of $20,000 is to be repaid with monthly payments over four years at an annual interest rate of 6%, compounded monthly. What is the monthly payment? How much interest is paid over the four years?

Chapter 5: Discrete Functions

Learning Goals and Expectations

Demonstrate an understanding of...Demonstrate an ability to...

The characteristics of discrete functions (e.g., domain; range; graph)Distinguish between discrete and continuous functions by examining their domains and graphs Recognize and describe arithmetic and geometric sequences and series using recursive and explicit formulas Calculate the nth term, the partial sum, and the infinite sum of arithmetic and geometric sequences and series Use sigma notation to represent arithmetic and geometric series Use discrete functions to model and analyze real-world situations (e.g., population growth; compound interest; annuities; mortgages)

Assessment Focus: Knowledge/Understanding; Thinking/Inquiry; Communication; Application

Assessment Methods: Quizzes; Tests; Assignments; Projects; Presentations

Assessment Criteria: Accuracy; Completeness; Clarity; Relevance

Assessment Tools: Rubrics; Checklists; Answer Keys

Assessment Feedback: Descriptive Feedback; Peer Feedback; Self-Assessment

Assessment Accommodations: Extra Time; Oral Responses; Scribe Services

Assessment Resources: Textbook; Calculator; Software; Internet

### Chapter 6: Financial Applications of Functions

#### Key Concepts

In this chapter, you will learn how to:

Review the concepts of simple interest and co