Math 142, Chapter 2 Spring 2011 Zarestky Chapter 2 Reading Notes In this chapter, we will review some important types of functions that will serve as the foundation for the calculus topics we will cover later on. None of Chapter 2 should be new to you; consider Chapter 2 to be a review. If you don’t remember what a function is or what it does, you will need to read Chapter 1 on your own and visit with me in office hours. You may also wish to review Chapter 1 as you complete the algebra review homework assignments in WebAssign. Section 2.2: Elementary Functions: Graphs and Transformations By the end of this section, you should be able to: • Recognize the graphs of the identity, square, cube, square root, cube root, and absolute value functions. • Develop and graph piece-wise functions to model real-world situations. Read the section up to “Vertical and Horizontal Shifts.” (About 2 pages.) This section begins by introducing the basic elementary functions. These functions serve as the building blocks for many other functions. Example 1 should be review. Skim it to make sure you understand. Note that the “Conceptual Insight” box shows you two equivalent ways to represent the absolute value function. Given a graph, you should be able to recognize the corresponding basic function and vice versa. Make notes about the function rules, graphs, and domain and range of the six basic elementary functions. What are the defining characteristics of each one? I.e., how can you tell them apart?Math 142, Chapter 2 Spring 2011 Zarestky Skip ahead to “Piecewise-Defined Functions” starting on p. 64 (We are not going to cover transformations of functions because we can do most of that work with our graphing calculators.) Read the rest of the section, up to the exercises. (About 1.5 pages.) Work Example 6. Compare your answers to the book’s solution. What questions do you have? Check your understanding of this section by working a few problems from the exercises on your own. Because we skipped some of this section, focus on 43-48, and 65-68. What questions do you still have?Math 142, Chapter 2 Spring 2011 Zarestky Section 2.3: Quadratic Functions By the end of this section, you should be able to: • Determine a quadratic model for a revenue or profit function and calculate the break-even point. If you are feeling rusty on quadratic functions, you may wish to read the first part of this section on your own. Otherwise, skip to the part titled Applications. In these examples, you will use the unique properties of quadratic functions to answer questions. Read Examples 3 and 4. Note that Examples 3 and 4 concern revenue, cost, profit, supply and demand, and break-even points. Make some notes about the meaning of those terms and the mathematical relationships among them. You may wish to refer to p. 51 on the book, or, if you’ve taken Math 141, you may wish to refer to your notes from that course. The following examples use a graphing calculator as a tool. Calculator help is linked from our course calendar page. Look for the help topics “graphing a function” and “intersection of functions”. Work Example 3. Compare your answers to the book’s solution. What questions do you have?Math 142, Chapter 2 Spring 2011 Zarestky Work Example 4. Compare your answers to the book’s solution. What questions do you have? Check your understanding of this section by working a few problems from the exercises on your own. Because we skipped some of this section, focus on 61-64. What questions do you still have?Math 142, Chapter 2 Spring 2011 Zarestky Section 2.5: Exponential Functions By the end of this section, you should be able to: • Distinguish between graphs of exponential functions with different bases and coefficients. • Simplify expressions using properties of exponents. • Solve problems involving compound interest. • Solve problems involving continuously compounded interest. • Model exponential growth and decay. Read the introductory text of this section through Theorem 1 and review Example 1. Make notes about the definition, graphs, and basic properties of exponential functions. Pay close attention to Figure 2 and Theorems 1 and 2. Read and make notes about base e exponential functions. Answer the Explore & Discuss 1 questions.Math 142, Chapter 2 Spring 2011 Zarestky Read the paragraph about Growth and Decay Applications. You should be able to use the term relative growth rate and understand what it means mathematically for a population to grow continuously. Work Example 2. Compare your answers to the book’s solution. What questions do you have? Work Example 3. Compare your answers to the book’s solution. What questions do you have?Math 142, Chapter 2 Spring 2011 Zarestky Read the paragraphs about Compound Interest. You should be able to use the terms interest rate, compound interest, principle, present value, and future value. If you have already taken MATH 141, these are the same terms and concepts you learned in that class. The difference is that now we will use the formulas instead of the TVM Solver on your graphing calculator. If you feel rusty using the TVM solver, calculator help is available online. Make notes about the compound interest formula and the variables used in the formula. Reference the summary table on p. 103 if needed. Work Examples 5 and 6. Compare your answers to the book’s solution. What questions do you have? Check your understanding of this section by working a few problems from the exercises on your own. Focus on 1-10, 29-38, and 43-52. What questions do you still have?Math 142, Chapter 2 Spring 2011 Zarestky Section 2.6: Logarithmic Functions By the end of this section, you should be able to: • Determine if a function is one-to-one. • Determine the inverse of a one-to-one function. • Convert between an exponential and a logarithmic equation. • Evaluate simple logarithmic expressions without a calculator. • Simplify logarithmic expressions using properties of logarithms. • Solve equations involving exponential functions. • Solve equations involving logarithmic functions. Much of this section should be review for you. In the following notes, I will ask you to read all of the material but spend the majority of your time on the