MATH& 144 - Precalculus I and II

1. Solve problems involving an understanding of the concept of a function and the related concepts of domain, range, composition of functions and inverse functions; and demonstrate understanding of these concepts using functions given in graphical, symbolic, or numerical form.
2. Correctly use mathematical notation and language related to the above concepts.
3. Graph a variety of functions and be able to interpret their graphs.
4. Formulate and apply properties, graphs, and some appropriate applications of linear, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
5. Solve equations and inequalities involving the aforementioned functions, both graphically and algebraically.
6. Demonstrate how and when to use technology as a tool in solving equations and investigating the behavior of functions and graphs.
7. Construct equations and functions involving the aforementioned functions that model situations described in words.
8. Solve problems involving right triangle trigonometry, the law of sines, and the law of cosines.
9. Distinguish identities from conditional equations, apply trigonometric identities to solve equations, and prove identities algebraically.
10. Solve problems involving the main graphical features of conic sections and the relationships between their graphs and equations.
11. Solve problems involving unit circle trigonometry.
12. Translate between graphical and algebraic representations, between the Cartesian and parametric representations of equations and graphs, and between polar and rectangular coordinates.
13. Recognize and sketch graphs of equations given in polar coordinates.
14. Perform vector operations, including vector algebra and dot product.
15. Use the above abilities to solve word problems and to express solutions clearly with correct use of mathematical notation and terminology.