Math 140: Unit 4

Target Date: Friday Oct. 2
Deadline: Tuesday Oct. 20

Note: The information on this page is for the 8th edition of the textbook.
Click here for the 7th edition information.
Click here for the 6th edition information.

Table of Contents:

Topics
Study Guidelines
Unit Pretest and Exam Description
Checklist

Topics

Unit 4 continues with the study of the concept of a function, one of the fundamental concepts of mathematics. As seen in the previous unit, one of the main methods of studying a function is by analyzing the graph of a function, which is a visual representation of the function. The first part of this unit analyzes the transformations of graphs produced by combining functions. This then leads into a more detailed study of the properties of combinations of functions. Finally, you will use the concept of a function to model and solve real-world applications.

• Transformations of Graphs (2.5)
  • Vertical and horizontal shifts
  • Vertical and horizontal stretches and compressions
  • Reflections
• Operations on Functions
  • Elementary operations: sum, difference, product, quotient (pages 57-58)
  • Composite functions (5.1)
  • Domain of a combination of functions (5.1)
• Mathematical Modeling and Applications
  • Setting up linear equations for applications (A.8)
  • Mathematical modeling: defining functions for use in applications (2.6)
  • Applications of linear functions (3.1)

Study Guidelines for the 8th edition of Sullivan's Precalculus

These reading and problem assignments are designed to help you learn the course material. You should complete all of these problems, check your answers in the back of the textbook, and get help with the problems that you missed. Most of the problems are odd-numbered, so you can check the solutions in the Solutions Manual.

The only way to learn mathematics is to do mathematics, so while these problems will not be collected or graded, you will probably not do well in the course if you do not complete these and check your work as described above. After completing these problems, go on to the Unit Exam Description below and follow directions.

• Section 2.5: Graphing Techniques: Transformations
  • Reading: section 2.5
    Read and work through examples 1-13 and their matched problems.
  • Try out some java applets that illustrate the various transformations:
    • vertical shifts
    • horizontal shifts
    • vertical stretching and reflection
    • horizontal stretching and reflection
  • Practice Problems: 2.5 #7-18, 19-33 odd, 35, 39, 41, 43, 45, 47, 53, 57, 61, 75-83 odds, 89, 91
    
    
• Sections 2.1 and 5.1: Operations on Functions; Composite Functions
  • Reading: Reread the "Form the Sum, Difference, Product, and Quotient of Two Functions" portion (pages 57-58) of section 2.1.
    Read and work through example 10 and its matched problem.
  • Practice Problems: 2.1 #61, 65, 69
  • Reading: section 5.1
    Read and work through examples 1-7 and their matched problems.
  • Try out a java applet that illustrates function composition.
  • Practice Problems: 5.1 #1-3, 7, 9, 11, 17, 19, 21, 23, 25, 27, 31, 33, 35, 41, 47, 49, 53, 55, 57, 65, 69, 71, 73, 75, 76
    
    
• Appendix A.8: Setting Up Equations; Applications
  • Reading: appendix section A.8
    Read and work through examples 1-8 and their matched problems.
  • Practice Problems: A.8 #7-33 odds, 37, 39, 41, 45, 47, 49, 53, 55
    
    
• Section 2.6: Mathematical Models: Constructing Functions
  • Reading: section 2.6
    Read and work through examples 1-3 and their matched problems.
  • Graphing calculator skills: Review appendix sections B.1-B.5. You will also need to learn how to use your graphing calculator to find the maximum or minimum of a function (see your calculator manual or Graphing Calculator Help).
  • Practice Problems: 2.6 #1, 5, 9, 11, 13, 18, 19, 21, 23
  • Practice Problems: 2.3 #63, 65
    
    
• Section 3.1: Linear Functions and their Properties
  • Reading: section 3.1, pages 122-123
    Read and work through examples 4-5 and their matched problems.
  • Practice Problems: 3.1 #37, 41, 47, 49
    
    
• Supplementary material (optional):
  • Student Solutions Manual
  • Algebra Review booklet
  • CD lecture series (step-by-step video examples on CD)
  • For tutoring help, visit the Prentice Hall Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need the access code that came with your textbook.
  • Graphing Calculator Help

Unit 4 Pretest and Exam Description

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 15 questions, and will count 15 points toward your grade. 
   • The exam has a one hour time limit.
   • You will need your graphing calculator on this exam. In particular, you will need to know how to use your graphing calculator to find the maximum or minimum of a function (as in many of the questions in section 2.6).
   • Many of the questions on this exam are multiple choice. For the other questions, be sure to look under the entry box for the expected format of the answer.
     • Some questions ask you for the formula of a function. In this case, simply type in the formula, such as x^2-4x. Do not include "f(x)=" in your answer.
     • Some of the questions on this exam ask for an approximation instead of an exact answer. These questions will ask you to give an answer that is "accurate to at least one decimal place" (or possibly two decimals, or three decimals, etc.). In this case, you would have to enter at least one digit after the decimal point. For example, if you calculate your answer to be 1.41421356237, then you could enter 1.4, 1.41, 1.414, 1.4142, etc. When you view your corrected exam, you will see that the "correct" answer is given in the form 1.4142  0.1. The symbol means "plus or minus", so anything within 0.1 of the first number counts as correct.
     • If a question does not ask for an approximation, then your answer must be exact.
2. Complete the online Unit 4 Pretest assignment. You may use your book and notes if you wish.
   • Directions: Click on the link above, then choose the Unit 4 Pretest.
   • The pretest must be completed by the deadline date listed at the top of this page.
     However, you may redo the pretest as many times as you like before the due date.
     Your best score counts, and it will be rescaled to 5 points maximum.
3. If you are having trouble with any of the problems listed above or on the pretest, make use of the help resources listed on the Help page.
4. Arrange with your proctor to take the online proctored Unit 4 Exam. Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.
   • Directions: Click on the link above, then choose Unit 4 Exam.
   • The proctored unit exam must be completed by the deadline date listed at the top of this page, and may be repeated under certain conditions. See the Detailed Schedule page for specific rules.

   Note: Remember that you can always go back and take practice exams on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

   • Directions: Click on the link above, then choose Unit 4 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 4 Checklist

To finish Unit 4, make sure that you have completed the following items:

• Read the material listed in the Study Guidelines.
• Practice the problems listed in the Study Guidelines, and use any of the listed supplementary material to help you understand the concepts.
• Complete the online Unit Pretest (read the exam description first).
• Complete the online proctored Unit Exam.

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