# MAT 153 Precalculus

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### Course Description

Topics include functions and their graphs; systems of linear and quadratic equations; ratios, proportion, variation; sequences; mathematical induction; the binomial theorem; complex numbers; theory of equations and trigonometry.

Satisfies the General Education Quantitative Reasoning Requirement.

4 units credit.

Included in the above list of topics are: domain, range, inverse functions. Standard algebraic transformations of functions and the corresponding geometric transformations of their graphs. Exponential and logarithmic functions and equations; exponential growth and decay. Right-triangle trigonometry and applications. Trigonometric and inverse trigonometric functions and their graphs. Harmonic motion and sinusoids. Trigonometric identities and equations. The laws of sines and cosines.

### Prerequisite

MAT 009 or equivalent.

### Text

Precalculus: a Prelude to Calculus (1st ed.), by Sheldon Axler. Wiley, 2009.

### Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

The course may be based on the following chapters in the text. Other topics may be included as time permits.

• 0. The Real Numbers
• 1. Functions and their Graphs
• 2. Linear, Quadratic, Polynomial, and Rational Functions
• 3. Exponentials, Logarithms, and e.
• 4. Trigonometric Functions
• 5. Trigonometric Algebra and Geometry.
• 6. Applications of Trigonometry

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

The final exam is given at the date and time announced in the Schedule of Classes.

### Learning Objectives

After completing MAT 153 the student will

• obtain the domain and graph of linear, quadratic, exponential, logarithmic, trigonometric, and inverse trigonometric functions
• use and understand the Vertical and Horizontal Line Tests
• find the composition of two functions algebraically, and the inverse of a function, both algebraically and geometrically
• demonstrate the effects of standard algebraic transformations on the graph of a function e.g. translation, reflection, rescaling
• use laws of exponents, logarithms, and trigonometric identities
• simplify expressions involving exponential, logarithmic, and trigonometric functions
• solve exponential, logarithmic, and trigonometric equations
• prove trigonometric identities
• solve standard exponential growth and decay problems
• demonstrate the correspondence between the symmetries of the trigonometric circle and the symmetries of the trigonometric functions
• use a graphing calculator or computer to graph and evaluate exponential, logarithmic, and trigonometric functions
• solve triangles using the Laws of Sines and Cosines
• apply trigonometry to surveying, navigation, area, and angular speed problems and harmonic oscillations
• correctly use standard mathematical notation and terminology and avoid nonsensical expressions and statements throughout the course.

### Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

### Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

### Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

### Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Prepared by F. Brulois. Revised 1/2/01 (F. Brulois), 7/6/01, 7/25/06, 2/8/13, 1/7/15 (G. Jennings).