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Precalculus
Submission Information

Final

Mathematics

April 30, 2012
Descriptor Details

Precalculus

155


4.0
Preparation for calculus: polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions and their graphs; analytic geometry, polar coordinates
Trigonometry
 Functions including linear, polynomial, rational, radical, exponential, absolute value, logarithmic, trigonometric; definitions, evaluation, domain and range;
 Inverses of functions;
 Algebra of functions;
 Graphs of functions including asymptotic behavior, intercepts, and vertices;
 Transformations of quadratic, absolute value, radical, rational, logarithmic, exponential functions;
 Equations including rational, linear, radical, polynomial, exponential, trigonometric, logarithmic, and absolute value;
 Linear, nonlinear, and absolute value inequalities;
 Systems of equations and inequalities;
 Characterization of real and complex zeros of polynomials;
 Unit circle and right triangle trigonometry;
 Trigonometric and inverse trigonometric identities and formulas;
 Graphing trigonometric functions: period, amplitude, phase shift, inverse trigonometric functions; and
 Polar coordinates
Upon successful completion of the course, students will be able to:
 Graph functions and relations in rectangular coordinates and polar coordinates;
 Synthesize results from the graphs and/or equations of functions and relations;
 Apply transformations to the graphs of functions and relations;
 Recognize the relationship between functions and their inverses graphically and algebraically;
 Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic, and solve linear, nonlinear, and absolute value inequalities;
 Solve systems of equations and inequalities;
 Apply functions to model real world applications;
 Identify special triangles and their related angle and side measures;
 Evaluate the trigonometric function of an angle given in degree and radian measure;
 Manipulate and simplify a trigonometric expression;
 Solve trigonometric equations, triangles, and applications;
 Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs; and
 Prove trigonometric identities
Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.
A college level text designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.