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Intermediate Algebra

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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, and 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. Rectangular coordinates, angles and circular/radian measure;
11. Definitions of the six trigonometric functions according to the right triangle, the unit circle, and the rectangular coordinate system;
12. Applications of the right triangle;
13. Simplification of trigonometric expressions;
14. Proofs of trigonometric identities;
15. Graphs of trigonometric functions: period, amplitude, phase shift, and asymptotes;
16. Inverse trigonometric functions, identities, and graphs;
17. Solving Triangles: Law of Sines and Law of Cosines;
18. Polar coordinates and equations;
19. DeMoivre’s Theorem and applications; and
20. Introduction to vectors.

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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. Prove trigonometric identities;
9. Identify special triangles and their related angle and side measures;
10. Evaluate the trigonometric function at an angle whose measure is given in degrees and radians;
11. Manipulate and simplify a trigonometric expression;
12. Solve trigonometric equations, triangles, and applications;
13. Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs;
14. Evaluate and graph inverse trigonometric functions;
15. Convert between polar and rectangular coordinates;
16. Calculate powers and roots of complex numbers using DeMoivre’s Theorem; and
17. Represent a vector (a quantity with magnitude and direction) in the form <a,b> and ai+bj.

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.