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 application (word) problems at the end of
the section.
Read the introductory text and the section titled Inverse Functions. Make notes about the
definition of one-to-one functions and the inverse of a function. The technique we will use to
graphically determine if a function is one-to-one is the horizontal line test. If any horizontal line
passes through the graph of a function no more than once, then that function has an inverse.
Read the section titled Logarithmic Functions up to the section titled Applications (about 6
pages). Make notes about the definition and properties of logarithmic functions and evaluating
logarithms on a calculator.
Work through examples 1-9 to refresh your memory. Do you have any questions?
Math 142, Chapter 2
Spring 2011
Zarestky
Work Example 10. 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 1-33(odd), 43-51(odd), 57-73(odd), 79-84. (If you don’t have time for much,
choose at least one problem from each group.)
What questions do you still have?