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Precalculus: Graphs & Models
Tutorials
Software Steps to
access the textbook Calculator
/ Graphing Utility
Review
Materials
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This course emphasizes topics that form the foundation for study of electronics, engineering technology, game and simulation programming, and calculus. Topics include analyzing and graphing quadratic, polynomial, rational, exponential, logarithmic and trigonometric functions; solving systems of equations with matrices; and developing complex solutions to problems in rectangular, trigonometric and Euler form. Students use computer software and technology to assist in problem solving and analysis. Prerequisite: Successful completion of MATH-104 or MATH-114, or equivalent performance on placement examinations. This course is not self-paced. Follow the Course Schedule to stay on track.
A note about
the course syllabus and general course layout...
All student
objectives, assignments or expectations can be identified by
either a light blue shaded background or bolded blue text.
DeVry University Online course content is constructed from curriculum guides developed for each course that are in alignment with specific Terminal Course Objectives. The Terminal Course Objectives (TCOs) define the learning objectives that the student will be required to comprehend and demonstrate by course completion. The TCOs that will be covered in detail each week can be found in the Objectives section for that particular week. Whenever possible, a reference will be made from a particular assignment or discussion back to the TCO that it emphasizes.
| 1 |
Given a relation, determine whether it is a function and, if it is, determine its domain and range. Identify intervals of increasing, decreasing, and constant y values as well as the relation’s symmetry – if any – and classify it as an even or odd function where applicable. |
| 2 |
Given the equation of a polynomial function of up to fifth order, with a maximum of two non-rational roots, a rational function with a denominator of order two or less, or a radical function, predict the function behavior based on information gathered about predictors such as the axis intercepts, far end behavior and asymptotes, as appropriate. Use technology to verify the predictions and to graph the function. |
| 3 |
Given a real-world applied problem formulate an appropriate exponential equation and solve using the laws of exponents and properties of logarithms. Use composition to show that exponential and logarithmic functions are inverses. |
| 4 |
Given the graph or
equation of a polynomial, simple rational (denominator with
degree
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| 5 |
Given a 2x2 or 3x3 systems of linear equations and unknowns, solve for the unknown variables using algebraic techniques, matrix methods such as the inverse of the coefficient matrix and Gaussian elimination, and appropriate technological tools to arrive at a solution. Use technology to solve larger systems and/or real world problems with real world numbers. |
| 6 |
Use right angle trigonometry to solve right triangles that relate to real world problems. |
| 7 |
Given the
trigonometric functions |
| 8 |
Given a linear
conditional trigonometric equation, solve for the unknowns over
the interval |
| 9 |
Define and plot on the complex plane. Express complex numbers in rectangular, polar, and Eüler form. Perform elementary algebraic operations on complex numbers. |
),
simple radical, trigonometric, exponential, or logarithmic
function, translate this function using reflections across the
axes, horizontal and vertical shifts, stretching and shrinking.
Use technology to demonstrate the relationship between the
graphs and the underlying functions.
,
graph the function. Establish the reciprocal, Pythagorean
and other basic identities. Define the inverse
trigonometric functions.
.
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Week |
Readings |
Assignments |
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Week 1 |
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TCO 5 |
Chapter R: Basic Concepts of
Algebra (Sections R.2-R.7)
PDF | HTML
Chapter 1, Part 1: Graphics,
Functions, and Models (Section 1.3)
PDF | HTML
Chapter 1, Part 2: Graphics,
Functions, and Models (Sections 1.3-1.4)
PDF | HTML
Chapter 2, Part 1: Functions,
Equations, and Inequalities (Section 2.3)
PDF | HTML
Chapter 2, Part 2: Functions,
Equations, and Inequalities (Sections 2.3-2.5)
PDF | HTML
Chapter 8: Systems of Equations and Matrices (Sections 8.1-8.4) PDF | HTML |
MML:
eCollege:
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Week 2 |
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TCO 1 TCO 2 TCO 4 |
Chapter 1, Part 1: Graphics,
Functions, and Models (Section 1.2)
PDF | HTML
Chapter 1, Part 2: Graphics,
Functions, and Models (Sections 1.5 & 1.7)
PDF | HTML
Chapter 3: Polynomial and Rational Functions (Sections 3.1, 3.2, 3.4, 3.5) PDF | HTML |
MML:
eCollege:
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Week 3 |
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TCO 1 TCO 3 TCO 4 |
Chapter 4: Exponential and Logarithmic Functions (Sections 4.1-4.6) PDF | HTML |
MML:
eCollege:
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| Week 4 | ||
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TCO 6 |
Chapter 5, Part 1: The Trigonometric Functions (Sections 5.1-5.4) PDF | HTML |
MML:
eCollege:
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| Week 5 | ||
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TCO 1 TCO 4 TCO 7 |
Chapter 5, Part 2: The Trigonometric Functions (Sections 5.5
& 5.6)
PDF | HTML
Chapter 6: Trigonometric Identities, Inverse Functions, and Equations (Sections 6.1 & 6.4) PDF | HTML |
MML:
eCollege:
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| Week 6 | ||
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TCO 7 TCO 8 |
Chapter 6: Trigonometric Identities, Inverse Functions, and Equations (Sections 6.2 & 6.5) PDF | HTML |
MML:
eCollege:
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| Week 7 | ||
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TCO 9
Complex Numbers in Trigonometric Form Polar Coordinates and Graphs |
Chapter 7: Applications of Trigonometry (Sections 7.3-7.4) PDF | HTML |
MML:
eCollege:
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| Week 8 | ||
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TCO ALL |
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MML:
eCollege:
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The maximum score in this class is 1,000 points. The categories, which contribute to your final grade, are weighted as follows:
|
Assignment |
Points |
Weighting |
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Discussions |
77 |
7.7% |
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Homework |
294 |
29.4% |
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Quizzes |
84 |
8.4% |
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Tests |
315 |
31.5% |
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Final Exam |
230 |
23% |
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Total Points |
1000 |
100% |
DeVry University Online is an intense learning environment. Thus, late work poses a serious threat to a student’s ability to keep up with the pace of this course. There are times, however, when students may fall behind due to unforeseen circumstances. As a rule, late work is unacceptable, but the instructor recognizes that sometimes emergencies prevent students from completing their work on time. In the event that the student cannot submit his/her work on time he/she should contact the instructor immediately. The instructor reserves the right to deduct points for the late submission.
Cutoff time for assignment postings is 12 midnight Mountain Time the day the assignment is due.
One final note: Please note that technical problems are not excuses for late assignments in this class. Please back up your work in several places: your system, a floppy or Zip disk, email the file to yourself at another e-mail account, etc. There is nothing worse than losing hard work to a computer crash, and such issue will not constitute a valid excuse for late work in this class. Students are expected to take the necessary steps to ensure the timeliness of their work. Play it safe!
All of your course requirements are graded using points. At the end of the course, the points are converted to a letter grade using the scale in the table below. You must obtain an overall course average of 70% or above in order to pass the course.
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Letter Grade |
Points |
Percentage |
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A |
900 - 1000 |
90% to 100% |
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B |
800 - 899 |
80% to 89% |
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C |
700 - 799 |
70% to 79% |
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F |
699 - and below |
Below 70% |
For DVUO policy on assignment values and letter grades (and all other DVUO policies), please review the information contained in "Policies" under the Course Home section of your course.
In the "Discussion" areas of the course, you, as a student, can interact with your instructor and classmates to explore questions and comments related to the content of this course. Discussions will always close Sunday, 11:59 P.M. Mountain Time (MT).
A successful student in online education is one who takes an active role in the learning process. You are therefore encouraged to participate in the discussion areas to enhance your learning experience throughout each week.
The discussions will be graded for:
1. Frequency—Number and regularity of your discussion comments, and
2. Quality—Content of your contributions
Frequency—Number and regularity of your contributions. Students are expected to log into the course and post (respond) in the discussion topics on a minimum of three separate days per week, beginning no later than Wednesday.
Quality—Content of your contributions. Examples of quality posts include:
- providing additional information to the discussion;
- elaborating on previous comments from others;
- presenting explanations of concepts or methods to help fellow students,
- presenting reasons for or against a topic in a persuasive fashion,
- sharing your own personal experiences that relate to the topic, and
- providing a URL and explanation for an area you researched on the Internet.
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Quality Measurement |
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High
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Your contributions to each Topic indicate your mastery of the materials assigned. Your responses might integrate multiple views and/or show value as a seed for reflection for other participants' responses to the thread. You provide evidence that you are reading the assigned materials and other student postings and are responding accordingly, bringing out interesting interpretations. You know the facts and are able to analyze them and handle conceptual ideas. |
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Medium
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Your responses build on the ideas of another participant (or more) and dig deeper into assignment questions or issues. When you make intelligent posts during the week, including some good critique of the course material, then you have demonstrated you have an understanding of the material, are reading posts of your colleagues, and are contributing to the class. Your posts demonstrate confidence with the materials, but may be just a bit off target in one area or another. |
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Low
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You have meaningful interaction with other participants' postings. Posts that state I agree or I disagree include an explanation of what is disagreed or agreed upon and why, or introduce an argument that adds to the discussion. However, you may have rambling, lengthy posts that show no sign of having been re-read and refined before posting, and your writing suffers lack of clarity and comprehension. |
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Unsatisfactory
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You will receive little credit in the week's discussion by just showing up and making trivial comments, without adding any new thought to the discussion. At the low end of the spectrum, no participation gets a "0." If you are not in the discussion, you do not earn any points. |
Full credit is awarded when both high quality and required frequency is met.
For DVUO policy on discussions (and all other DVUO policies), please review the information contained in "Policies" under the Course Home section of your course.
Threaded Discussions:
Each week you will have a graded threaded discussion assignment. The weekly discussions are designed to enhance and solidify your understanding of the course material in an interactive forum different from MyMathLab. Your thoughtful participation and meaningful contribution are expected. Each week contains one graded topic and the ungraded Q&A Forum. Week 1 also contains a Classmate Introduction topic, which is required but not graded. You are expected to contribute to the class discussions on at least three different days, with a total of at least three substantial and relevant posts in each graded topic. You are required to participate in the threaded discussions each week, Weeks 1-7. Participation in Week 8 is optional.
Where do you need the practice? Where can you offer a small step or a suggestion to help? What tricks do you already know, and what do we need to review? Let's talk to each other and take turns! Keep your contributions small and manageable, and use words to explain your math, so everyone can follow your train of thought and think of ways to build on your contribution.
Please do not answer a whole question all by yourself -- the questions posted are usually multi-part questions designed to give a team of classmates an opportunity to earn posting points while working together on unraveling the mystery! Once a question has been answered to everyone's' satisfaction, and we have moved on please do not answer it again -- instead, participate in solving a new problem!
Note: Feel free to post screenshots of question from the Review assignments, HW, Practice Final Exam assignment, or Study Plan at any time to the threads. However, be advised that you may not make copies of Quiz, Test, or Final Exam questions. You may ask about similar questions from your Study Plan, but you may not disclose the actual Test or Exam questions in the threads.
Review Assignment
The Review Assignment is recommended but not graded. This assignment is located in the HW area of MML, to allow you take advantage of the Show-Me-How Features as you review. You may work on this assignment as often as you like; a minimum score of 80% is recommended to demonstrate mastery in the basic Algebra skills required as a foundation before you start this course.
To help you brush up on things you may have forgotten, without putting you behind in Week 1, we have made the review material available to you in MML during Preview Week for the course, although it is not recommended until Week 1. College Algebra and Trigonometry is a very demanding course, and there is very little time in Week 1 for reviewing all that material -- you must do this on your own, and it is best done early!
Homework
Each week you will have one HW assignment (see the Assignment page for each week). Your HW assignment for any given week is located in MML under the respective week heading, and must be completed inside MML. You will not submit your assignments to a Dropbox in eCollege. MML provides you with resources and instant help features such as links to the relevant sections in your eBook, sections videos, and guided examples on how to solve problems like the HW problems.
HW assignments are located in MML. You have unlimited retakes and must pass all HW assignments with a score of 80% or better. The HW assignment for the week is due by Sunday, end of week, 11:59 p.m. (MT). After the due date, zeros will be entered into MML for the missing homework assignments.
Quizzes
Each week you will have one quiz assignment (see the Assignment page for each week). Your quiz assignment for any given week is located in MML under the respective week heading, and it must be completed inside MML. You will not be completing any quizzes inside eCollege. You will work each quiz immediately after successfully completing the corresponding HW assignment.
If, after completing the corresponding HW assignment, you do not pass a quiz with at least 80%, you should go into the Study Plan in MML for the appropriate Chapter and Section and work a few practice problems. MML provides you with resources and instant help features, such as links to the relevant sections in your eBook, sections videos, and guided examples on how to solve problems like the quiz problems.Quiz assignments are located in MML. You have unlimited retakes and must pass all quiz assignments with a score of 80% or better. All quiz assignments for the week are due by Sunday, end of week, 11:59 p.m. (MT). After the due date, zeros will be entered into MML for the missing quiz assignments.
Tests
Every other week you will have one test. Your test for any given week is contained in MML under the respective week heading, and must be completed there. You will not be completing any tests inside eCollege. The test covers the material from the quizzes and HW from the previous 2 weeks, as well as material from previous weeks. Since you must complete all HW and quizzes with a minimum score of 80%, we anticipate that your score on the weekly test should be around 80% or better, as well.
You may take a test up to two times in the week it is assigned. The highest score counts. You are expected to consult your Study Plan and work practice problems to help you review the skills you have not yet mastered, before you retake the test. Your test is due by Sunday, end of week, 11:59 p.m. (MT). After the due date, zeros will be entered into MML for the missing Weekly Test. If the instructor grants you permission to take an exam late, you will only be given one .
Final Exam
You will take the comprehensive Final Exam in Week 8. The final exam may not be taken early. The Final Exam is contained in MML under the Week 8 heading, and it must be completed there. You will not be completing the Final Exam inside eCollege. You are expected to practice for the Final Exam with the Practice Final Exam Assignment in Weeks 6, 7, and 8. While you must score a minimum of 70% on the Practice Final Exam Assignment to be able to take the Final Exam, you are encouraged to strive for a score of 80% or better to give yourself the best possible preparation for the Final Exam. You may rework incorrect problems on the Practice Final Exam Assignment as many times as you want in Weeks 6, 7, and 8.
You may take the Final Exam up to two times in Week 8. The highest score counts. You are expected to consult your Study Plan and work problems within the Practice Final Exam Assignment to help you review the skills you have not yet mastered, before you retake the Final Exam. Your Final Exam is due by Thursday in Week 8, 11:59 p.m. (MT). The final exam will close after the due date, and you may no longer work on it.
Plagiarism
Plagiarism is a violation of the Academic Integrity code of this institution and will not be tolerated. The plagiarism policy applies to every aspect of DVUO coursework including threaded discussions, exams, quizzes, essays, assignments, etc. It is important that students fully cite any outside ideas, text and visual aides they reference in that work.
If you copy from, rely on, or paraphrase from your text or from any other source, you must include in-text citations and complete end-of-text citations. For any source, you must include the proper reference material including the full URL and date accessed if the source is from the Web. For help, see the APA Citation Policy and Materials section below. Failure to cite completely in-text and at the end of the paper is a violation of DeVry Academic Standards. Instructors are required to follow the DeVry Academic Integrity Policy. Refer to your Student Handbook or the Policy tab under Course Home to read the policy.
As a part of our commitment to academic integrity, your work in this course may be submitted to turnitin.com, an online plagiarism checking service. Turnitin.com operates a secure database and protects your privacy by assigning report numbers to all student work stored in its database. The purpose of using this service is to help protect the integrity of a DeVry degree, which in turn helps to protect your work and your investment in a DeVry education. See Turnitin.com for more details.
For a complete explanation of DeVry University Online's Academic Integrity Policy, please see the Policies item under the Course Home tab. For additional information see your student handbook, which is available in the Student Services website.
APA Citation Policy and Reference Materials
The DVUO citation policy is that all undergraduate students should use APA citation style for all DeVry Online undergraduate assignments and projects. If you have questions, we recommend using the following APA reference materials.
| APA Reference Materials | |
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Frequently Asked Questions
When are grades calculated, and how can I view my grades?
- You must complete any quizzes and post your written assignments (if necessary) to the weekly Dropbox by Sunday 11:59 p.m. (MT) each week, except Week 8 which closes at 11:59 p.m. (MT) Thursday.
- Once your work is reviewed, you should see comments and total points for each assignment in the Gradebook. Instructors should have Discussion work graded by the following Tuesday and all other assignments by the following Friday.
- You may check your progress at any time by going to the Gradebook, selecting the week and then your name.
- Click on the points earned for each assignment in the Gradebook to see any instructor comments.
What should I do if a discrepancy is found with my grade?
- Double-check the error and try to determine what caused it.
- Send your instructor an email explaining your findings.
- Trust that any error in grading will be corrected quickly.
What if I cannot get my work submitted on time?
- If you have an emergency that will cause your work to be late, please contact your instructor in advance of the due date so that arrangements can be made. Your instructor may reserve the right to deduct points for work turned in late based on the reason and the timeliness of notice.
- If a technical problem prevents you from meeting the scheduled due date, please contact the Help Desk at 1-800-594-2402 and immediately email your instructor about the situation.
What should I do if I have a disability that requires accommodation?
DeVry Online is committed to providing reasonable accommodations for eligible students with documented disabilities as defined by state and federal laws relating to the Americans with Disabilities Act (ADA). Our intent is to ensure that every student who makes a request for accommodations under ADA is advised of the accommodation process as promptly as possible. If you are a student with a verifiable documented disability, and you can provide medical documentation regarding this disability, then contact our ADA Officer at adaofficer@devry.edu for more information on how to receive ADA accommodations in your online classes or fax your request to 630-929-9745.
How can I get extra credit?
It is the policy of DeVry University that extra credit will not be allowed in any of its classes, online or onsite, for any reason.