Functions 11 McGraw-Hill: A Review of the Textbook
Functions 11 McGraw-Hill is a mathematics textbook designed for students in grade 11 who are studying functions. The textbook covers various topics such as linear and quadratic functions, exponential and logarithmic functions, trigonometric functions, polynomial and rational functions, and discrete functions. The textbook also includes chapters on transformations, sequences and series, and combinatorics.
The textbook aims to help students develop their mathematical skills and understanding through a variety of features, such as:
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- Prerequisite skills review at the beginning of each chapter
- Examples with detailed solutions and explanations
- Practice questions with answers at the end of each section
- Problem solving strategies and tips
- Technology applications using graphing calculators, spreadsheets, and software
- Real-world connections and applications
- Cumulative reviews and chapter tests
- Appendices with reference materials and additional practice
The textbook is based on the Ontario mathematics curriculum for grade 11 university preparation courses. It is written by a team of experienced mathematics educators and authors, such as George Knill, Chris Kirkpatrick, Marian Small, and others. The textbook is published by McGraw-Hill Ryerson, a leading publisher of educational resources in Canada.
Functions 11 McGraw-Hill is available in both print and digital formats. The print version can be ordered from the publisher's website or from other online retailers. The digital version can be accessed through the ConnectED platform, which provides interactive features such as videos, animations, quizzes, and feedback. The digital version also allows students to access the textbook anytime and anywhere using their devices.
Functions 11 McGraw-Hill is a comprehensive and engaging textbook that supports students' learning of functions in grade 11. It provides clear explanations, examples, and practice questions that help students master the concepts and skills. It also integrates technology and real-world contexts that make mathematics relevant and meaningful. Functions 11 McGraw-Hill is a valuable resource for students who want to succeed in their mathematics courses and prepare for their future studies.
In this section, we will review some of the main topics and features of the textbook. We will also provide some examples and questions from the textbook to illustrate the content and style of the textbook.
Linear and Quadratic Functions
The first chapter of the textbook introduces the concept of functions and how to represent them using different forms, such as equations, tables, graphs, and function notation. The chapter also explains how to identify the domain and range of functions, and how to determine the number of zeros and the maximum or minimum value of a quadratic function. The chapter also explores how to transform quadratic functions and how to solve problems involving the intersection of a linear and a quadratic function.
For example, one of the questions in the chapter asks students to find the equation of a quadratic function that has the same zeros as f(x) = x^2 - 5x - 6 and passes through the point (2, 5). The solution is as follows:
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- Since f(x) has the same zeros as the given function, we can write f(x) = a(x + 1)(x - 6), where a is a constant.
- To find the value of a, we can substitute x = 2 and f(x) = 5 into the equation and solve for a.
- f(2) = a(2 + 1)(2 - 6) = 5
- a(-4)(3) = 5
- a = -5/12
- Therefore, f(x) = -5/12(x + 1)(x - 6)
- We can expand this expression to get f(x) = -5/12x^2 + 25/6x + 5/2
This question demonstrates how to use function notation, factoring, substitution, and algebraic manipulation to find the equation of a quadratic function given some information about it.
Exponential and Logarithmic Functions
The second chapter of the textbook covers exponential and logarithmic functions and their properties. The chapter explains how to graph exponential and logarithmic functions using transformations and asymptotes. The chapter also shows how to solve exponential and logarithmic equations using equivalent forms, inverse operations, and common bases. The chapter also applies exponential and logarithmic functions to model real-world situations such as population growth, radioactive decay, pH levels, and sound intensity.
For example, one of the questions in the chapter asks students to determine how long it takes for a sample of uranium-238 to decay to half its original mass. The solution is as follows:
- We can use the formula A = A_0e^(-kt) to model the decay of uranium-238, where A is the mass after t years, A_0 is the original mass, k is the decay constant, and e is the base of natural logarithms.
- We can find the value of k by using the fact that uranium-238 has a half-life of 4.47 billion years. This means that A = A_0/2 when t = 4.47 billion.
- A_0/2 = A_0e^(-k(4.47 billion))
- Dividing both sides by A_0 and taking natural logarithms of both sides, we get ln(1/2) = -k(4.47 billion)
- Solving for k, we get k = -ln(1/2)/(4.47 billion)
- k â 1.55 x 10^-10
- Therefore, A = A_0e^(-1.55 x 10^-10t)
- To find how long it takes for A to be half of A_0, we can set A = A_0/2 again and solve for t.
- A_0/2 = A_0e^(-1.55 x 10^-10t)
- Dividing both sides by A_0 and taking natural logarithms of both sides, we get ln(1/2) = -1.55 x 10^-10t
- Solving for t, we get t = -ln(1/2)/(1.55 x 10^-10)
- t â 4.47 billion
This question demonstrates how to use exponential functions,
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