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This book gives you 500 questions that cover the most essential concepts in elementary and intermediate precalculus and in much of advanced precalculus. In the Answers section, for each problem, you’ll find a detailed way to reach the solution. The questions and solutions will give you valuable independent practice to supplement your regular textbook and the ground you have already covered in your precalculus class.
Basic Algebraic Skills.
Working with Real Numbers.
Complex Numbers.
The Cartesian Coordinate System.
Precalculus Function Skills.
Basic Function Concepts.
Operations with Functions.
Graphs of Functions.
Basic Graphing Concepts.
Increasing and Decreasing Behavior and Extrema.
Function Transformations.
Linear and Quadratic Functions, Equations, and Inequalities.
Linear Functions.
Linear Equations and Inequalities.
Quadratic Functions.
Quadratic Equations and Inequalities.
Average Rate of Change and Difference Quotients for Linear and Quadratic Functions.
Linear and Quadratic Function Models and Applications.
Polynomial and Rational Functions.
Polynomial Functions.
Remainder Theorem, Factor Theorem, and Fundamental Theorem of Algebra.
Descartes’ Rule of Signs and Rational Root Theorem.
Rational Functions.
Vertical, Horizontal, and Oblique Asymptotes and Holes in Graphs of Rational Functions.
Behavior of Polynomial and Rational Functions Near ±∞.
Exponential, Logarithmic, and Other Common Functions.
Exponential Functions.
Logarithmic Functions.
Exponential and Logarithmic Equations.
Other Common Functions.
Matrices and Systems of Linear Equations.
Basic Concepts of Matrices.
Determinants and Inverses.
Solving Systems of Linear Equations Using Inverse Matrices.
Solving Systems of Linear Equations Using Cramer’s Rule.
Solving Systems of Linear Equations Using Elementary Row Transformations.
Sequences, Series, and Mathematical Induction.
Sequences.
Mathematical Induction.
Trigonometric Functions.
Angle Measurement.
Trigonometric Functions.
Trigonometric Graphs and Transformations.
Analytic Trigonometry.
Fundamental Trigonometric Identities.
Sum and Difference Identities.
Double- and Half-Angle Identities.
Trigonometric Equations.
Solving Triangles