Course Syllabus

 

Course Description:

Preparation for calculus: polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions and their graphs; analytic geometry, polar coordinates.

 

Student Learning Outcomes:

 

Upon successful completion of the course, students will be able to:

  1. Graph functions and relations in rectangular coordinates and polar coordinates;
  2. Synthesize results from the graphs and/or equations of functions and relations;
  3. Apply transformations to the graphs of functions and relations;
  4. Recognize the relationship between functions and their inverses graphically and algebraically;
  5. Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic, and solve linear, nonlinear, and absolute value inequalities;
  6. Solve systems of equations and inequalities;
  7. Apply functions to model real world applications;
  8. Identify special triangles and their related angle and side measures;
  9. Evaluate the trigonometric function of an angle given in degree and radian measure;
  10. Manipulate and simplify a trigonometric expression;
  11. Solve trigonometric equations, triangles, and applications;
  12. Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs; and
  13. Prove trigonometric identities

Course Content:

 

  1. Functions including linear, polynomial, rational, radical, exponential, absolute value, logarithmic, trigonometric; definitions, evaluation, domain and range;
  2. Inverses of functions;
  3. Algebra of functions;
  4. Graphs of functions including asymptotic behavior, intercepts, and vertices;
  5. Transformations of quadratic, absolute value, radical, rational, logarithmic, exponential functions;
  6. Equations including rational, linear, radical, polynomial, exponential, trigonometric, logarithmic, and absolute value;
  7. Linear, nonlinear, and absolute value inequalities;
  8. Systems of equations and inequalities;
  9. Characterization of real and complex zeros of polynomials;
  10. Unit circle and right triangle trigonometry;
  11. Trigonometric and inverse trigonometric identities and formulas;
  12. Graphing trigonometric functions:  period, amplitude, phase shift, inverse trigonometric functions; and
  13. Polar coordinates

Textbook, used in addition to Dr.'s Notes:

Great news: your textbook for this class is available for free online!

Precalculus from OpenStax, ISBN 1-947172-06-9

You have several options to obtain this book:

  • View online (Links to an external site.) (Links to an external site.)
  • Download a PDF (Links to an external site.) (Links to an external site.)
  • Order a print copy (Links to an external site.) (Links to an external site.) 

You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.