College Algebra Study Guide

Real Numbers, Algebraic Expressions, and Operations

Master properties of real numbers, simplifying expressions, factoring techniques, and polynomial operations essential for all subsequent topics.

Exponents, Radicals, and Rational Expressions

Simplify expressions with integer and rational exponents, radicals, and complex fractions frequently tested on final exams.

Linear Equations and Inequalities

Solve linear equations, absolute value equations, compound inequalities, and model real-world problems with linear relationships.

Functions: Definitions, Notation, and Graphs

Understand domain, range, function notation, piecewise functions, and interpreting graphs—the foundation for advanced function analysis.

Transformations, Combinations, and Inverse Functions

Apply shifts, stretches, reflections; perform function composition; find and verify inverse functions for exam success.

Polynomial Functions and Equations

Graph polynomials, find zeros using synthetic division, apply the Fundamental Theorem of Algebra and Rational Root Theorem.

Rational Functions and Their Graphs

Identify vertical, horizontal, and slant asymptotes, holes, and intercepts to accurately graph and analyze rational functions.

Exponential Functions and Applications

Model growth, decay, and compound interest; solve exponential equations critical for science and finance word problems.

Logarithmic Functions and Equations

Apply logarithm properties, solve logarithmic equations, and use change-of-base formula for complex exam calculations.

Systems of Equations and Inequalities

Solve systems using substitution, elimination, and matrices; graph linear inequalities and solve application problems.

Sequences, Series, and Conic Sections

Work with arithmetic and geometric sequences, summation notation, and identify equations of circles, parabolas, ellipses, hyperbolas.

Introduction to Trigonometry

Master the unit circle, right-triangle trigonometry, basic identities, and radian measure preparing for calculus readiness.