VIRGINIA HIGHLANDS COMMUNITY COLLEGE
COURSE OF
STUDY
MTH
163 Precalculus Mathematics I FALL
2008
INSTRUCTOR:
Susan Clark Fleming
Office: OTC 1218 e-mail: sfleming@vhcc.edu
Web Page- www.vhcc.edu/sfleming Phone: 276-739-2513
COURSE DESCRIPTION:
This course presents college algebra, matrices, and algebraic, exponential, and logarithmic functions. Prerequisites: a placement recommendation for MTH 163 and Algebra I, Algebra II, and Geometry or equivalent. (Credit will not be awarded for both MTH 163 and MTH 166.) Lecture 3 hours per week.
BROAD GOALS:
Goals of the course are to gain conceptual and analytical understanding of the nature and behavior of linear, quadratic, polynomial, rational, exponential, and logarithmic functions, applications of functions, the modeling of real-world phenomena by functions. Appropriate use of technology will be employed in such a way as to enhance, as opposed to substituting for, analytical and conceptual competence.
SPECIFIC OBJECTIVES:
Linear and Quadratic Functions
1. Given a linear function in any form, put it into the slope-intercept form and use the slope and intercept to construct a graph of the function.
2. For a linear function y = mx + b, determine the value of y corresponding to a given value of x, or the value of x corresponding to a given value of y.
3. For a given quadratic function determine its vertex and zeros and without making a table construct a reasonable sketch of the graph of the function.
4. For a given function determine the average rate of change of the dependent variable with respect to the independent variable between any two given points, and explain the interpretation of this rate as the slope of the graph.
Rates of Change
1. For a given function representing a real-world situation determine the average rate of change of the dependent variable with respect to the independent variable between any two given values of the independent variable, and explain the interpretation of this rate specifically within the given context.
2. For a given function representing the rate at which a given quantity changes determine the approximate change in that quantity between two given values of the independent variable, and interpret this change as the area of a trapezoid.
3. Know the definition of the average rate of change of a function. Use and interpret the difference quotient.
Solving Equations and Inequalities
1. Solve given linear, quadratic, algebraic, exponential and logarithmic equations.
2. Write and solve linear, quadratic, algebraic, exponential and logarithmic equations corresponding to real-world applications and situations, and interpret the results.
3. Solve linear and quadratic inequalities and construct graphs of the solutions.
Characteristics of Functions, Graphs, Combining Functions
1. Construct graphs of linear, quadratic, power and exponential functions without using tables, using knowledge of the basic behavior of the given function and the graph stretching/shifting effects of the various parameters that define the specific function.
2. Know the basic "Library of Functions": the power functions for powers –1 to 3, the reciprocal function, the absolute value function, the greatest integer function, and piecewise functions.
3. Determine if a given function is increasing, decreasing, even or odd; know the mathematical definitions of these terms.
4. Give the algebraic form of the sum, difference, product, quotient or composite of two given functions.
5. From the graphs of two given functions construct the graph of the sum, difference, product, quotient or composite of two functions.
Exponential Functions, Inverse Functions, Logarithmic Functions
1. Be able to identify the growth rate, growth factor and initial value of a given exponential function; or interpret an applied situation to find these quantities.
2. Given information from which growth rate, growth factor and initial value of an exponential function can be determined, write the corresponding exponential function.
3. Construct the graph of an inverse function from the given function.
4. Given an equation defining a function determine the equation of the inverse function.
5. Determine whether a given pair of functions are inverses.
6. Know and be able to apply the laws of exponents and logarithms.
7. Switch an equation from logarithmic to exponential form or vice versa.
8. Apply exponential and logarithmic functions as appropriate to situations involving compound interest, decibel scales, and exponential growth and decay.
Polynomial Functions
1. Know the statement of the Fundamental Theorem of Algebra and its implications for the graphs of polynomials.
2. From factored form determine the zeros of a polynomial function and the nature of the zeros, the large-|x| behavior, the y intercept and construct a reasonable representation of the graph of the function.
3. Be able to represent all possible forms of the graph of a polynomial of given degree.
4. Given a rational function determine its zeros, vertical asymptotes, horizontal asymptotes and oblique asymptotes, and large-|x| behavior and construct a reasonable graph to represent the function.
5. Obtain real or complex solutions, as appropriate, to quadratic equations.
6. Find the real and complex roots of a polynomial.
7. Obtain real or complex solutions, as appropriate, to quadratic equations.
8. Find the real and complex roots of a polynomial.
Basic Theorems
1. Know and be able to apply the Remainder Theorem, Factor Theorem, Rational Zeros Theorem, and the Intermediate Value Theorem, and be able to determine bounds on the zeros of a polynomial function.
Systems of Equations, Matrices, Matrix Algebra, Systems of Inequalities
1. Solve systems of simultaneous equations using substitution, elimination, matrix reduction, determinants or inverse matrices as requested.
2. Given an applied problem involving linear relationships among two or more variables, set up a system of simultaneous equations to represent the problem.
3. Given a set of simultaneous linear equations, represent the system as a matrix equation; given a matrix equation write the corresponding system of linear equations.
4. Know and be able to apply the basic theorems relating the changes of values of determinants to the various row or column operations.
5. Know and be able to apply or prove the properties of matrix algebra.
6. Solve systems of nonlinear equations using substitution and/or elimination.
7. Graph inequalities and/or systems of inequalities.
8. Set up and solve linear programming problems related to applied situations.
UNITS TO BE COVERED:
Chapter 1 - Graphs, Functions, and Models
Chapter 2 – More on Functions
Chapter 3 – Quadratic Functions and Equations; Inequalities
Chapter 4 - Polynomial and Rational Functions
Chapter 5 - Exponential and Logarithmic Functions
Chapter 9 - Systems of Equations and Matrices
METHODS and GRADING
1. Daily homework assignments will be made to provide practice on the material covered in class. Answers for many problems are located in the back of the book. It is the student's responsibility to come for help as needed. Students may also e-mail questions to sfleming@vhcc.edu.
2. Section quizzes will be given on blackboard throughout the semester. The quizzes will be based on the homework assignments from the previous class period. Students have until the beginning of the class period after that section was assigned to complete the quiz. The purpose of these quizzes is to encourage you to keep up with your assignments and to seek help on the problems BEFORE the next class period. Because the purpose of the quizzes is to encourage you to keep up with your work, these quizzes cannot be made up if you don’t get them done on time. You may take each quiz twice. The highest grade will count.
3. Tests will be given periodically throughout the semester. See Course Schedule in Bb for dates.
4. A comprehensive final will be required of all students. This counts 25% of the final grade. The exam will be given only on the date published in the Course Schedule.
5. Absolutely no make-up tests are given. The exam grade will be substituted for any missed tests. If you know you will be absent when a test is scheduled, you can make arrangements to take the test early. For students who do not miss any tests, the exam grade will be substituted for the lowest test grade if the exam grade is higher than the test grade.
6. Cheating in any form will not be tolerated. Any student caught cheating will receive a grade of F in the course and will be sent before the Student Judiciary Committee fro appropriate disciplinary action. Cheating includes giving as well as receiving aid on any test, quiz, or hand-in assignment. Plagiarism will be handled in the same manner.
7. The course grade will be determined as follows:
Quizzes 25%
Tests 50%
Final Exam 25%
Grading Scale:
90-100 A
80-89 B
70-79 C
60-69 D
Below 60 F
W-The college has a strict policy for withdrawing from classes and receiving a grade of W. Students who simply quit coming and do not formally withdraw will receive a grade of F.
INSTRUCTIONAL MATERIAL
TEXT: Precalculus: Graphs & Models (4th ed.), Bittinger, Beecher, Ellenbogen, Penna. Pearson, 2009. (ISBN 0321525345)
CALCULATOR: A graphing calculator, preferably the TI-84, is required for this class. If you use another model, you must know how to operate it with no help from the instructor.
OFFICE HOURS
MW 9:30-11:00AM and 2:45-4:15PM
CLASSROOM ETIQUETTE
It is the instructor’s responsibility to maintain a classroom environment conducive to learning. Students who are disruptive will be asked to leave the classroom and may not be allowed to return. Be respectful of your fellow students. Even if you know what is going on, talking to your neighbor may disturb someone else who is trying to learn.
Cell phones are to be turned off and put away at the beginning of class. Answering a cell phone during class or text messaging during class may result in the student being asked to leave the classroom.
Use of iPods or other headphone devices in class is prohibited.
IMPORTANT DATES FOR FALL 2008
Monday, August 25 Classes Begin
Monday, September 1 Labor Day - College closed - No classes
Thursday, September 11 Last day to add/drop a course, change from audit to credit, and receive tuition refund
Friday, October 3 Faculty in-service - No classes
Thursday, October 30 Last day to withdraw from class without academic penalty or change from credit to audit
Wednesday, November 26 Faculty in-service - No classes
Thurs-Fri, Nov 27-28 Thanksgiving holidays - College closed - No classes
Monday, December 1 Open enrollment for all spring semester begins
Friday, December 12 Last day of classes
Wednesday, December 17 Final Exam (10:30 AM-1:00 PM)
Instructor reserves the right to make changes in the syllabus.