MISSOURI SOUTHERN STATE UNIVERSITY COURSE SYLLABUS

Transcription

1 MISSOURI SOUTHERN STATE UNIVERSITY COURSE SYLLABUS SCHOOL: Arts and Sciences DEPARTMENT: Mathematics COURSE NUMBER: Math 130 COURSE TITLE: College Algebra COURSE CIP NO: CREDIT: 3 PREPARED BY: Tran van Thuong UPDATED BY: Charles Curtis DATE APPROVED BY DEPARTMENT: Orig Date 2006 Rev. Date March 2011 SIGNATURE: Department Head COURSE DESCRIPTION FOR CATALOG Math 130 (Fall, Spring) 3 hrs. cr. College Algebra A study of functions and their graphs, including linear and quadratic, polynomial, rational, exponential, and logarithmic functions. Prerequisites: A Math ACT score of 22 (or higher) or MATH 030 with a grade of C or better. 1

2 OBJECTIVES Numbers in brackets reference General Education Goals. The student will: 1. Understand the concept of function, and be able to apply the properties of functions and their graphs. Specifically, know and apply properties of the following types of functions and their graphs: linear and quadratic functions, piecewise defined functions, higher order polynomial functions, rational functions, exponential and logarithmic functions. [7 B E] 2. Solve the following types of equations and inequalities: linear equations and inequalities, absolute value equations and inequalities, quadratic equations and inequalities, polynomial and rational equations and inequalities, exponential and logarithmic equations. [7 B E] 3. Use functions and their graphs to model application problems and draw mathematical conclusions about these applications. [7 B E] 4. Use a graphing calculator to solve application problems in a real world context. [7 B E] COURSE OUTLINE The student will: Chapter F: Foundations: A Prelude to Functions F.1 The Distance and Midpoint Formulas Topic Obj F.1a Know and be able to apply the Pythagorean Theorem, Distance Formula, and Midpoint Formula. F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry Topic Obj F.2a Determine, from an equation in two variables, intercepts and symmetries of the graph and whether a given point is on the graph of the equation. F.3 Lines Topic Obj F.3a Determine the slope of a line, given the graph of the line or two points on the line, or an equation of the line. Topic Obj F.3b Determine an equation of a line, given such information as two points on the line, a point on the line and a line perpendicular, etc. Topic Obj F.3c Graph a line given its equation. F.4 Circles Topic Obj F.4a Determine the equation of a circle in both standard form and general form given information about the graph of the circle. Topic Obj F.4b Find information about the graph of a circle from its equation. 2

3 Chapter 1: Functions and Their Graphs 1.1 Functions Topic Obj 1.1a: Understand the concept of function and be able to evaluate functions and find their domains. 1.2 The Graph of a Function Topic Obj 1.2a: Topic Obj 1.2b: 1.3 Properties of Functions Topic Obj 1.3a: Topic Obj 1.3b: Determine when a graph is a function. Obtain information, including function values, domain and range, intercepts, points of intersection with lines, and zeros from and about the graph of a function. Determine from the graph of a function properties of the graph such as intervals of increase and intervals of decrease and local maxima and minima. Determine from the formula for a function, with the aid of a graphing calculator, properties of the graph such as intervals of increase and intervals of decrease and local maxima and minima. 1.4 Library of Functions; Piecewise defined Functions Topic Obj 1.4a: Graph the following functions without a calculator: mx + b, x 2, x 3, x, Topic Obj 1.4b: 3 x, 1 x, and x. 1.5 Graphing Techniques: Transformations Topic Obj 1.5a: Write the formula for a piecewise defined function from its graph, and be able to draw the graph of a piecewise defined function from its formula. Understand the concept of transformation (shifting, reflecting, stretching, and shrinking), and be able to apply this understanding to draw graphs and identify graphs. 3

4 Chapter 2: Linear and Quadratic Functions 2.1 Properties of Linear Functions Topic Obj 2.1a: Solve linear equations. Topic Obj 2.1b: Understand the relationship between linear functions and straight lines and apply such knowledge. 2.2 Building Linear Functions from Data; Direct Variation Topic Obj 2.2a: Use a graphing calculator to find a linear regression model for a data set. Topic Obj 2.2b: Use the model to solve real world applications 2.3 Quadratic Functions and Their Zeros Topic Obj 2.3a: Solve quadratic equations using a variety of techniques including factoring, the square root method, completing the square, and the quadratic formula. Topic Obj 2.3b: Solve equations that are quadratic form in form. 2.4 Properties of Quadratic Functions Topic Obj 2.4a: Determine properties of quadratic functions from a formula and from a graph. Topic Obj 2.4b: Graph a quadratic function. Topic Obj 2.4c: Construct a quadratic function possessing specified properties. 2.5 Inequalities Involving Quadratic Functions (covered in Section 3.4) 2.7 Complex Zeros of a Quadratic Function (covered in Section 3.6) 2.8 Equations and Inequalities Involving Absolute Value Function Topic Obj 2.8a: Solve absolute value equations and inequalities. 4

5 Chapter 3: Polynomial and Rational Functions 3.1 Polynomial Functions and Models Topic Obj 3.1a: Understand the properties and graphs of polynomial functions, and construct a polynomial function that has a given graph. Topic Obj 3.1b: Understand the meaning of zeros of polynomial functions and their connection to the graphs of these functions. 3.2 Properties of Rational Functions Topic Obj 3.2a: Solve a rational equation. Topic Obj 3.2b: Understand the properties and graphs of rational functions, and generate appropriate information such as asymptotes. 3.3 The Graph of a Rational Function; Inverse and Joint Variation Topic Obj 3.3a: Draw the graph of a rational function from its formula, and be able to construct a rational function that has a given graph. 3.4 Polynomial and Rational Inequalities Topic Obj 3.4a: Solve polynomial and rational inequalities. 3.5 The Real Zeros of a Polynomial Function Topic Obj 3.5a: Understand the meaning of the Remainder Theorem and its application to evaluating polynomial functions. Topic Obj 3.5b: Understand the meaning of the Factor Theorem and its application to solving polynomial equations. 3.6 Complex Zeros; Fundamental Theorem of Algebra Topic Obj 3.6a: Perform operations involving complex numbers. Topic Obj 3.6b: Understand the importance of the Fundamental Theorem of Algebra, its application to polynomial equations, and its connection to complex numbers. 5

6 Chapter 4: Exponential and Logarithmic Functions 4.1 Composite Functions Topic Obj 4.1a: Form a composite function. Topic Obj 4.1b: Identify individual components of a composite function. Topic Obj 4.1c: Determine the domain of a composite function. 4.2 One to One Functions; Inverse Functions Topic Obj 4.2a: Determine whether a function is one to one from a graph. Topic Obj 4.2b: Determine the inverse of a one to one function given by a formula or a set of ordered pairs. Topic Obj 4.3c: Find the graph of the inverse function from the graph of the function. 4.3 Exponential Functions Topic Obj 4.3a: Understand the properties and graphs of exponential functions, and evaluate and graph such functions. 4.4 Logarithmic Functions Topic Obj 4.4a: Understand the relationship between logarithmic functions and exponential functions, and be able to evaluate and graph logarithmic functions. 4.5 Properties of Logarithms Topic Obj 4.5a: Understand the properties of logarithms and their relationship to exponentials, and perform operations on logarithms. 4.6 Logarithmic and Exponential Equations Topic Obj 4.6a: Apply properties of logarithms and exponents to solve exponential and logarithmic equations algebraically. 4.7 Compound Interest Topic Obj 4.7a: Understand the meaning of compound interest, and apply the knowledge of exponential functions to model this application. 4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay Topic Obj 4.8a: Understand the meaning of exponential growth and decay, and apply the knowledge of exponential and logarithmic functions to model such applications. 4.9 Building Exponential, Logarithmic, and Logistic Functions from Data Topic Obj 4.9a: Use a graphing calculator to find an exponential or logarithmic regression model for a data set. Topic Obj 4.9b: Use the model to solve real world applications 6

7 Optional Topics Within the above listed sections, the instructor may cover additional topic objectives. In addition, the instructor may choose to cover any of the sections listed below as time allows. Section 1.6 Construct functions to model applications and use those functions to answer questions relating to the applications. Section 2.6 Use technology to find a quadratic regression model for a data set. Use the model to solve real world applications. Chapter 5 Understand the properties and graphs of parabolas, ellipses, and/or hyperbolas, and perform basic related algebraic and graphing operations. Section 6.1 Solve systems of linear equations and use this knowledge to model applications. Sections Understand the concepts of matrices and their inverses, matrix operations, and determinants, and perform required computations involving matrices. Understand how matrices are used to model and solve systems of linear equations, and be able to apply this understanding. Section 6.6 Chapter 7 Solve systems of nonlinear equations. Understand the concepts of sequences and series and their applications, and perform related algebraic tasks. Understand and apply the Binomial Theorem. 7

8 TEXT AND LABORATORY MANUALS Rental: Sullivan, Michael, and Michael Sullivan III. College Algebra: Concepts Through Functions. 1 st ed. Upper Saddle River, NJ: Prentice Hall, Print. [ISBN 13: ] Purchase: MyMathLab Access Code TI 89 Titanium Graphing Calculator REFERENCES AVAILABLE IN THE LIBRARY Books: Larson, Ron, Robert Hostetler, and Anne Hodgkins. College Algebra: Concepts and Models, 3 rd ed. Boston: Houghton Mifflin, [QA154.2.L ] Aufmann, Richard N., Vernon Barker, and Richard Nation. College Algebra and Trigonometry. 2 nd ed. Boston: Houghton Mifflin, [QA154.2.A ] Journals: PROCEDURES Lectures, discussions, group work, board work, and/or internet resources. EVALUATION Examinations, class participation, homework, and/or quizzes may be included in the course grade. A comprehensive final examination is required of all students completing the course. AMERICANS WITH DISABILITIES (ADA) STATEMENT If you are an individual with a disability and require an accommodation for this class, please notify the instructor or Judy Elimelech, Disabilities Coordinator, at the Learning Center ( ). 8