Math 140: Unit 7

Target Date: Friday Nov. 6
Deadline: Friday Nov. 13

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 7 begins with appendix A.10 on the roots and rational exponents. This is a preparation for the materials in the later sections in this unit. In section 5.2, we study additional properties of graphs and functions, concentrating on inverse functions. The concept of inverse function will be used to define the logarithmic functions in section 5.4.

Although the book only covers rationalizing denominators, in some applications (e.g., in calculating derivatives in calculus) one may have to rationalize numerators. Therefore, we have included a page on rationalizing numerators.

• Rational Exponents (A. 10)
  • nth roots
  • simplifying radical
  • Rationalize Denominators and Numerators.
  • Solve Radical Equations
  • Simplify Expressions with Rational Exponents.
• Inverse Functions (5.2)
  • One-to-one functions, horizontal line test
  • Inverse of a one-to-one function
    • Properties of the inverse
    • Finding the inverse of a one-to-one function
• Exponential Functions (5.3)
  • Definition, base, domain, and range
  • Properties of graphs
  • Properties of exponential functions
  • Solving simple exponential equations
  • Base e
• Logarithmic Functions (5.4)
  • Definition (inverse of the exponential function), base, domain, and range
  • Properties of graphs
  • Properties of logarithmic functions
  • Natural logarithms
  • Solving simple logarithmic equations

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 A.10: nth roots; Rational Exponents
  • Review the laws of exponents in appendix A.1 before you begin this section.
  • Reading: appendix section A.10
    In addition, see the supplement on rationalizing numerators.
  • Practice Problems: A.10 #1, 2, 7-10, 11-39 odds, 45, 47, 49, 57, 61, 63, 69, 73, 75, 77, 81, 87, 91, 95, 101, 107
    
    
• Section 5.2: One-to-one Functions; Inverse Functions
  • Review sections 2.1-3 before you begin this section.
  • Reading: section 5.2
    Read and work through examples 1-11 and their matched problems.
    Be sure to know the procedure for finding the inverse of a function (page 257).
  • See the module on inverse functions for discussion of the concept, examples, and several animations and applets.
  • Practice Problems: 5.2 #1, 2, 3, 9, 11, 13, 15, 17-23, 27, 31-39 odds, 41-46, 47-69 odds
    
    
• Section 5.3: Exponential Functions
  • Review appendix A.1, A.6, A.10 and section 2.5 before you begin this section.
  • Reading: section 5.3
    Read and work through examples 1-8 and their matched problems.
    The properties of the exponential function are summarized on page 272.
  • Practice Problems: 5.3 #1-5, 11-19 odds, 21, 23, 29-33, 37, 43, 45, 46, 49, 51, 53, 57-75 odds, 77, 83, 85, 87, 89, 97, 99
    
    
• Section 5.4: Logarithmic Functions
  • Review appendix A.9 and section 3.5 before you begin this section.
  • Reading: section 5.4
    Read and work through examples 1-10 and their matched problems.
    The properties of the logarithmic function are summarized on page 285.
  • Try out a java applet that lets you explore the graphs of exponential and logarithmic functions.
  • Practice Problems: 5.4 #1, 2, 3, 9-51 odds, 59, 63-70, 71, 75, 81, 87, 91, 95, 97, 99, 103, 105, 109, 111,
    
    
• 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 7 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 graph logarithmic and exponential functions.
   • Be sure to look under the entry box for the expected format of the answer.
     • Some problems ask you to solve a problem which may have more than one solution. If there is more than one solution, separate the solutions with a semicolon. For example, your answer might be 3;5.
     • 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 two decimal places" (or possibly one decimal, or three decimals, etc.). In this case, you would have to enter at least two digits after the decimal point. For example, if you calculate your answer to be 1.41421356237, then you could enter 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  0.01. The symbol means "plus or minus", so anything within 0.01 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 7 Pretest assignment. You may use your book and notes if you wish.
   • Directions: Click on the link above, then choose the Unit 7 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 7 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 7 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 7 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 7 Checklist

To finish Unit 7, 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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