College Algebra II and Analytic Geometry
This course presents an extensive review of intermediate algebra topics. The review will include: solving linear equations and inequalities, fundamental concepts associated with quadratic equations, solving equations and inequalities with absolute values and other miscellaneous equations involving rational expressions and radical expressions. An introduction to complex number arithmetic is also included. Additionally, it covers general concepts associated with relations and functions. Topics such as the algebra of functions, function composition and range and domain are studied. The graphical representation of linear and quadratic functions are also presented. The algebraic and graphical representation of circles will also be studied as it pertains to terminology associated with relations in general. Basic graphical transformations are introduced. Polynomial and rational functions are studied in detail. In particular, ideas associated with zeros of polynomials, end-behavior, and graph sketching are discussed. Students will learn about synthetic division, the remainder theorem, the conjugate root theorem, horizontal and slant (oblique) asymptotes, and vertical asymptotes. Finally, exponential and logarithmic functions are studied in detail. Specific skills entail working with the rules of exponents and logarithms and solving exponential and logarithmic equations. Concepts associated with one-to-one functions and the existence of inverses are also studied. Sketching and recognizing the graphical representation of exponential and log functions is included.