Robert Blitzer's college algebra book — Blitzer Precalculus without trigonometry or the calculus preview.
Review of foundational algebra concepts students need before college algebra: real numbers, exponents and scientific notation, radicals and rational exponents, polynomials, factoring, and rational expressions.
Solving linear equations, rational equations, quadratic equations, equations with radicals, and equations quadratic in form. Modeling with equations. Complex numbers. Solving linear and absolute value inequalities. (Blitzer CollAlg expands the equations content from Blitzer Precalculus Ch P.7-P.9 into a full chapter.)
Functions, function notation, graphs, transformations of functions, combinations and composition of functions, inverse functions, distance and midpoint formulas, and circles.
Quadratic functions, polynomial functions and graphs, polynomial division and zeros, rational functions and asymptotes, polynomial and rational inequalities, and modeling with variation.
Exponential and logarithmic functions, properties of logarithms, solving exponential and logarithmic equations, and modeling with exponential growth and decay.
Systems of linear equations in two and three variables, systems of nonlinear equations in two variables.
Matrix solutions to linear systems via Gauss-Jordan elimination, matrix algebra (operations and inverses), determinants, and Cramer's Rule for 2x2 and 3x3 systems.
Conic sections in standard form: ellipse, hyperbola, and parabola. Identifying and graphing each conic given an equation; writing equations from key properties.
Sequences and series, arithmetic and geometric sequences, and the Binomial Theorem.