Module 1: Algebra Review (Chapter 1)
Section outline
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In the past few years, major earthquakes have occurred in several countries around the world. In January 2010, an earthquake of magnitude 7.3 hit Haiti. A magnitude 9 earthquake shook northeastern Japan in March 2011. In April 2014, an 8.2-magnitude earthquake struck off the coast of northern Chile. What do these numbers mean? In particular, how does a magnitude 9 earthquake compare with an earthquake of magnitude 8.2? Or 7.3?
Later in this chapter, we show how logarithmic functions are used to compare the relative intensity of two earthquakes based on the magnitude of each earthquake (see "Chapter Opener: The Richter Scale for Earthquakes" Example in Section 1.8: Logarithmic Functions).
Calculus is the mathematics that describes changes in functions. In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, exponential, and logarithmic functions. We review how to evaluate these functions, and we show the properties of their graphs. We provide examples of equations with terms involving these functions and illustrate the algebraic techniques necessary to solve them. In short, this chapter provides the foundation for the material to come. It is essential to be familiar and comfortable with these ideas before proceeding to the formal introduction of calculus in the next chapter.
Image Caption: A portion of the San Andreas Fault in California. Major faults like this are the sites of most of the strongest earthquakes ever recorded. (credit: modification of work by Robb Hannawacker, NPS)
(Content & Image Source: Chapter 1 Introduction, Calculus Volume 1, Gilbert Strang and Edwin "Jed" Herman, OpenStax, CC BY-NC-SA License)
Upon completion of this module, you will be able to:Section 1.1 Function
- Find function values.
- Graph functions and determine whether or not a graph is a function.
- Find the domain and range of the function.
Section 1.2 Operations on Functions
- Find the composition of the function using formulas and table
- Graph functions using vertical and horizontal shifts.
- Graph functions using reflections about the x-axis and the y-axis.
- Graph functions using compressions and stretches.
- Combine transformations.
Section 1.3 Linear Functions
- Graph equations of the types y= f(x)=b+mx, y= c and x=a
- Graph linear functions
- Find an equation of a line when given its slope and one point on the line and when given two points on the line
- Solve applied problems involving slope and linear functions.
Section 1.4 Exponents
- Simplifying exponential expressions involving rational and integer exponents
- Simplifying radical expressions
Section 1.5 Quadratics
- Learn basic concepts and different forms of a quadratic function and their graphs
- Solve problems involving quadratic equations
Section 1.6 Polynomials and Rational Functions
- Identify power functions.
- Identify end behavior of power functions.
- Identify polynomial functions.
- Identify the degree and leading coefficient of polynomial functions.
Section 1.7 Exponential Functions
- Evaluate exponential functions.
- Find the equation of an exponential function.
- Use compound interest formulas.
- Evaluate exponential functions with base e.
Section 1.8: Logarithmic Functions
- Convert from logarithmic to exponential form.
- Convert from exponential to logarithmic form.
- Evaluate logarithms.
- Use common logarithms.
- Use natural logarithms.
To achieve these objectives:- Read the Module 1 Introduction (see above).
- Read Sections 1.1 - 1.8 of Chapter 1: Algebra Review in Applied Calculus (links to each Section provided below)
- At the end of each Section there is a list of Vocabulary, a Self Check Quiz, and a set of Flashcards
- At the end of each Section there is a list of Vocabulary, a Self Check Quiz, and a set of Flashcards
- Watch the Videos for each Section (links provided below)
- Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
- Practice the problems on the Chapter 1 Review Exercises, checking the solutions provided (link provided below)
- Complete the MyOpenMath Quizzes for Chapter 1 (link provided below) - These are graded!
- Once you complete the Quizzes, upload your work in the Quiz Work Upload Assignment using the submission link below.
- Post in the Chapter 1 Q&A Discussion Forum - link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.
Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.
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