 # Syllabus for College Algebra

 Course Information Prerequisite (s): Grade of C or better in Mathematics 99 or Mathematics 112, or placement test, or consent of Department Chairperson Credit Hours: Four (4) Truman College General Education Goals Truman College General Education Goals for this course: • Goal 2 –The student performs effectively in the workplace and has the ability to work and make effective use of a wide variety of current technologies. • Goal 4 – The student demonstrates the ability to think critically, abstractly, and logically. • Goal 6 – The student demonstrates the ability to work independently. Course Description College Algebra: Math 140 emphasizes the notion of a function as a unifying concept. The following families of functions and their characteristics are examined within this course: polynomial, rational, exponential and logarithmic functions. Additional topics will include solving inequalities and systems of non -linear equations. Technology and writing assignments will be used throughout the course as appropriate. Applications involving problem-solving skills will be emphasized throughout the course. Course Objectives This course will provide you to: 1. Analyze the graphs of various families of functions. 2. Apply the models and characteristics of various families of functions to scenarios in order to solve real-world (contextual) problems. Student Learning Outcomes Students will be able to: Polynomial Functions and Models 1. Identify the characteristics of a quadratic function (i.e., vertex, axis of symmetry, and direction of concavity). 2. Compute roots/zeroes of a polynomial function by factoring techniques. 3. Estimate the roots/zeroes of a polynomial function. 4. Solve polynomial inequalities. 5. Solve systems of linear equations using matrices and determinants. 6. Solve systems of linear inequalities. 7. Solve systems of non-linear equations. Rational Functions and Models 8. Simplify rational expressions using the division algorithm . 9. Identify points of discontinuity of a rational function. 10. Identify vertical/horizontal asymptotes and end behavior of rational functions. 11. Solve rational inequalities. Power Functions and Models 12. Solve radical equations and equations with fractional exponents. 13. Identify the domain, range of power functions; determine if the function has an inverse. Find the inverse and its domain and range, if appropriate. Exponential and Logarithmic Functions and Models 14.Define exponential and logarithmic functions. 15. Simplify exponential and logarithmic expressions using their properties 16. Solve exponential and logarithmic equations. 17. Formulate and apply exponential and logarithmic functions to a contextual situation. It is expected that the following student learning outcomes (Characteristics of Functions) will be embedded as appropriate in the study of the family of functions listed above. • Identify the domain and range of a function. • Determine intervals on which functions are decreasing/increasing, continuous/non-continuous, or piecewise. • Identify functions from multiple sources of information (i.e., verbal descriptions, graphs, equations, and tables of values ). • Relate the effect of transformations (i.e., translations, rescaling, or reflections) on graphs of functions and their corresponding equations. • Perform operations (i.e., addition, subtraction, multiplication and division) on functions, including the composition of functions. • Decompose a function into a composition of two or more functions . • Formulate and apply a function to a contextual situation. • Determine the conditions under which a function has an inverse. • Identify the inverse of a function from multiple representations. • Reformulate a given function into various representations (i.e., verbal, graphical, algebraic, or tabular).

 Class Schedule – Math140 Truman College – Fall 2009 Week Date Topic 1 Monday August 24 Information and Policies Introduction to MML Using the TI-83/84 Graphical Calculator (See Appendix B page AP-4 – AP-10) Review ~ Factoring 1.1 Numbers, Data, and Problem Solving Wednesday August 26 1.2 Data Trends: Visualization of Data 1.3 Functions and Their Representations 1.4 Types of Functions and Their Rates of Change Chapter Review 2 Monday August 31 2.1 Linear Functions and Models 2.2 Equations of Lines Wednesday Sept. 2 2.3 Linear Equations 3 Monday Sept. 7 NO SCHOOL – Labor Day Holiday Wednesday Sept. 9 2.4 Linear Inequalities 2.5 Piecewise-Defined Functions Chapter Review 4 Monday Sept. 14 Exam #1 (will cover Chapters 1 and 2) Wednesday Sept 16. 3.1 Quadratic Concepts: Functions and Models 3.2 Quadratic Equations and Problem Solving 5 Monday Sept. 21 3.3 Quadratic Inequalities 3.4 Transformation of Functions Chapter Review Wednesday Sept. 23 4.1 Nonlinear Functions and Their Graphs 4.2 Polynomial Functions and Models 6 Monday Sept. 28 Exam #2 (will cover Chapter 3) Wednesday Sept. 30 4.3 Real Zeros of Polynomial Functions 7 Monday October 5 4.4 The Fundamental Theorem of Algebra: Non-Real Roots of a Polynomial Equation Wednesday October 7 4.5 Rational functions and models 8 Monday October 12 4.6 Polynomial and Rational Inequalities Wednesday October 14 4.7 Power Functions and Radical Equations Chapter Review 9 Monday October 19 5.1 Combining Function Wednesday October 21 5.2 Inverse Functions 10 Monday October 26 Exam #3 (will cover Chapter 4) Wednesday October 28 5.3 Exponential Functions 11 Monday November 2 5.4 Logarithmic Functions 5.5 Properties of Logarithms Wednesday November 4 5.6 Exponential and Logarithmic Equations 12 Monday November 9 5.7 Constructing Nonlinear Models Chapter Review Wednesday November 11 6.1 Functions and Equations in Two Variables 6.2 Systems of Equations and Inequalities in Two Variables 13 Monday November 16 Exam #4 (will cover Chapter 5) Wednesday November 18 6.3 System of Linear Equations in Three Variables 14 Monday November 23 6.4 Solutions to Linear Systems Using Matrices 6.5 Properties and Applications of Matrices Wednesday November 25 6.6 Inverse of Matrices 15 Monday November 30 6.7 Determinants Chapter Review Wednesday December 2 Optional: CHAPTER R.2 ~ The Equations and Graphs of the Circles 16 Monday December 7 Final Exam Review Wednesday December 9 FINAL EXAM (Part 1 & Part 2) Part 1: Departmental Exam of 10 Multiple Choice Questions (comprehensive) Part 2: Instructor-Created Exam (comprehensive)
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