Intermediate Algebra Student Workbook

Scottsdale Community CollegeIntermediate AlgebraStudent WorkbookDevelopment TeamDonna GaudetWilliam MeachamJenifer BohartAmy VolpeLinda KnopDonna GuhseThird Edition2013Intermediate Algebra Student Workbook by Scottsdale Community College is licensed under aCreative Commons Attribution-ShareAlike 3.0 Unported License.

About this WorkbookThis workbook was created by mathematics instructors at Scottsdale Community College inScottsdale, Arizona. It is designed to lead students through Intermediate Algebra, and to helpthem develop a deep understanding of the concepts. The included curriculum is broken intotwelve lessons. Each lesson includes the following components:MINI-LESSON The Mini-Lesson is the main instructional component for each lesson.Ideas are introduced with practical applications.Worked Examples are provided for each topic in the Mini-Lesson. Read through theseexamples carefully. Use these as a guide for completing similar problems.Media Examples are to be completed by watching online videos and taking notes/writingdown the problem as written by the instructor. Video links can be found athttp://sccmath.wordpress.com/mat09x/ or may be located within the Online HomeworkAssessment System.You-Try problems help reinforce Lesson concepts and should be worked in the orderthey appear showing as much work as possible. Answers can be checked in Appendix A.PRACTICE PROBLEMS This section follows the Mini-Lesson. If you are working through this material on yourown, the recommendation is to work all practice problems. If you are using this materialas part of a formal class, your instructor will provide guidance on which problems tocomplete. Your instructor will also provide information on accessing answers/solutionsfor these problems.LESSON ASSESSMENT The last part of each Lesson is a short assessment. If you are working through thismaterial on your own, use these assessments to test your understanding of the lessonconcepts. Take the assessments without the use of the book or your notes and then checkyour answers. If you are using this material as part of a formal class, your instructor willprovide instructions for completing these problems.ONLINE HOMEWORK ASSESSMENT SYSTEM If you are using these materials as part of a formal class and your class utilizes an onlinehomework/assessment system, your instructor will provide information as to how toaccess and use that system in conjunction with this workbook.

Table of ContentsLesson 1 – Introduction to Functions . 1Mini-Lesson 1 .3Section 1.1 – What is a Function? .3Section 1.2 – Multiple Representations of Functions .7Section 1.3 – Function Notation. 11Section 1.4 – Domain and Range . 17Section 1.5 – Applications of Functions . 20Lesson 1 Practice Problems . 27Lesson 1 Assessment . 53Lesson 2 – Functions and Function Operations . 55Mini-Lesson 2 . 57Section 2.1 – Combining Functions . 57Section 2.2 – Applications of Function Operations. 65Section 2.3 – Composition of Functions . 67Section 2.4 – Applications of Function Composition . 70Lesson 2 Practice Problems . 73Lesson 2 Assessment . 87Lesson 3 – Linear Equations and Functions . 89Mini-Lesson 3 . 91Section 3.1 – Linear Equations and Functions . 91Section 3.2 – Graphs of Linear Functions . 97Section 3.3 – Horizontal and Vertical Lines . 100Section 3.4 – Writing the Equation of a Line . 102Lesson 3 Practice Problems . 111Lesson 3 Assessment . 127Lesson 4 – Linear Functions and Applications . 129Mini-Lesson 4 . 131Section 4.1 – Review of Linear Functions . 131Section 4.2 – Average Rate of Change. 133Section 4.3 – Scatterplots on the Graphing Calculator . 139Section 4.4 –Linear Regression . 141Section 4.5 – Multiple Ways to Determine the Equation of a Line . 146Lesson 4 Practice Problems . 147Lesson 4 Assessment . 167Lesson 5 – Introduction to Exponential Functions . 169Mini-Lesson 5 . 171Section 5.1 – Linear Functions vs. Exponential Functions . 171Section 5.2 – Characteristics of Exponential Functions . 178

Section 5.3 – Solving Exponential Equations by Graphing . 181Section 5.4 – Applications of Exponential Functions . 185Lesson 5 Practice Problems . 189Lesson 5 Assessment . 201Lesson 6 – More Exponential Functions . 203Mini-Lesson 6 . 205Section 6.1 – Writing Exponential Models . 205Section 6.2 – Doubling Time and Halving Time . 208Section 6.3 – Exponential Regression . 214Lesson 6 Practice Problems . 217Lesson 6 Assessment . 231Lesson 7 – Logarithms and Logarithmic Functions . 233Mini-Lesson 7 . 235Section 7.1 – Introduction to Logarithms . 235Section 7.2 – Computing Logarithms . 238Section 7.3 – Characteristics of Logarithmic Functions . 243Section 7.4 – Solving Logarithmic Equations . 246Section 7.5 – Solving Exponential Equations Algebraically and Graphically . 250Section 7.6 – Using Logarithms as a Scaling Tool . 253Lesson 7 Practice Problems . 255Lesson 7 Assessment . 273Lesson 8 – Introduction to Quadratic Functions . 275Mini-Lesson 8 . 277Section 8.1 – Characteristics of Quadratic Functions . 277Section 8.2 – Solving Quadratic Equations Graphically . 285Section 8.3 – Applications of Quadratic Functions . 287Section 8.4 – Quadratic Regression . 291Lesson 8 Practice Problems . 293Lesson 8 Assessment . 309Lesson 9 – Solving Quadratic Equations . 311Mini-Lesson 9 . 313Section 9.1 – Quadratic Equations in Standard Form . 313Section 9.2 –Factoring Quadratic Expressions . 316Section 9.3 – Solving Quadratic Equations by Factoring . 320Section 9.4 –The Quadratic Formula . 324Section 9.5 – Complex Numbers. 327Section 9.6 – Complex Solutions to Quadratic Equations . 330Lesson 9 Practice Problems . 333Lesson 9 Assessment . 347

Lesson 10 – Radical Functions . 349Mini-Lesson 10 . 351Section 10.1 – Roots, Radicals, and Rational Exponents . 351Section 10.2 – Square Root Functions – Key Characteristics . 354Section 10.3 – Cube Root Functions – Key Characteristics . 356Section 10.4 – Radical Functions – Key Characteristics . 358Section 10.5 – Solve Radical Equations by Graphing . 360Section 10.6 – Solve Radical Equations Algebraically . 362Lesson 10 Practice Problems . 367Lesson 10 Assessment . 381Lesson 11 –Rational Functions . 383Mini-Lesson 11 . 385Section 11.1 – Characteristics of Rational Functions . 385Section 11.2 – Solving Rational Equations . 389Section 11.3 – Applications of Rational Functions . 394Lesson 11 Practice Problems . 397Lesson 11 Assessment . 409Lesson 12 – Course Review . 411Mini-Lesson 12 . 413Section 12.1 – Overview of Functions . 413Section 12.2 – Solving Equations . 419Section 12.3 – Mixed Applications . 421Lesson 12 Practice Problems . 429Lesson 12 Assessment . 459Appendix A: You-Try Answers. 461

Lesson 1 – Introduction to FunctionsThroughout this class, we will be looking at various Algebraic Functions and the characteristicsof each. Before we begin, we need to review the concept of what a Function is and look at therules that a Function must follow. We also need to investigate the different ways that we canrepresent a Function. It is important that we go beyond simple manipulation and evaluation ofthese Functions by examining their characteristics analyzing their behavior. Looking at theFunctions modeled as Graphs, Tables and Sets of Ordered Pairs is critical to accomplishing thatgoal.Lesson Topics:Section 1.1 What is a function? Definition of functionIndependent and Dependent VariablesSection 1.2 Multiple Representations of Functions Sets of ordered pairs (input, output)TablesGraphsVertical Line TestBehavior of GraphsSection 1.3 Function Notation Function evaluationWorking with input and outputMultiple RepresentationsUsing your graphing calculator to create graphs and tablesSection 1.4 Domain and Range DefinitionsMultiple RepresentationsRestricting Domain and Range (calculator)Section 1.5 Applications of Functions Criteria for a good graphPractical Domain and RangePage 1

Lesson 1 ChecklistComponentRequired?Y or TestPracticeProblemsLessonAssessmentPage 2DueScore

Name:Date:Mini-Lesson 1Section 1.1 – What is a Function?Intermediate Algebra is a study of functions and their characteristics. In this class, we will studyLINEAR, EXPONENTIAL, LOGARITHMIC, QUADRATIC, RATIONAL, & RADICALfunctions. Before we learn the specifics of these functions, we need to review/learn the languageand notation of FUNCTIONS.What is a Function?The concept of “function” is one that is very important in mathematics. The use of this term isvery specifi

Third Edition 2013 Intermediate Algebra Student Workbook by Scottsdale Community College is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. About this Workbook This workbook was created by mathematics instructors at Scottsdale Community College in Scottsdale .