1. Functions and Linear 1.1 Function and Relations.......................................12 1.2 Transformation...................................................22 1.3 The Slope of a Line.............................................37 1.4 Graphs of Linear Functions.................................42 1.5 Finding an Equation of the Line..........................49 1.6 Two linear Graphs...............................................55 1.7 Piecewise Function.............................................60 1.8 Absolute value function......................................64 1.9 Absolute Value equations and Inequalities...........71 2. Systems and Matrices 2.1 Systems of Linear Equations...............................80 2.2 Word Problems about System..............................90 2.3 Systems of Inequalities.......................................104 2.4 Linear Programming...........................................109 2.5 Algebra of Matrices............................................114 2.6 Inverse and Matrix Equation...............................121 3. Factoring and Expanding Polynomials 3.1 Law of Exponents...............................................128 3.2 Polynomials........................................................136 3.3 Multiplying Polynomials......................................139 3.4 Factoring using GCF...........................................151 3.5 Factoring Quadratic...........................................155 3.6 Factoring Polynomials........................................164 3.7 Solving Polynomial Equations..............................173 3.8 Word Problems about Polynomial Equation..........179 3.9 Solving polynomial Inequalities...........................188 4. Quadratic Function 4.1 Imaginary Numbers............................................194 4.2 Complex numbers...............................................199 4.3 Graphing Quadratic Functions............................208 4.4 Vertex of Quadratic Graphs................................217 4.5 Word Problems about Optimization.....................228 4.6 Finding Zeros by Factoring.................................238 4.7 Finding Zeros by Completing the Square.............243 4.8 Quadratic Formula.............................................248 4.9 Solving Equations in Quadratic Form...................253 4.10 Quadratic Inequalities using graphs...................258 4.11 Discriminant....................................................266 4.12 Sum and product of the roots...........................276 5. Polynomials 5.1 Graphing Polynomials.........................................284 5.2 Dividing Polynomials..........................................290 5.3 The Remainder and Factor Theorems..................297 5.4 Theorems about Roots of Polynomial..................302 5.5 Complex Roots of Polynomial function................308 6. Rational Expressions 6.1 Rational Expressions...........................................314 6.2 Multiplying and Dividing Rational Expressions......321 6.3 Sums and Differences of Rational Expressions.....324 6.4 Complex Fractions..............................................330 6.5 Rational Equations and Word Problems................336 6.6 Graph of Rational Functions...............................346 7. Radicals 7.1 Roots of Real Numbers.......................................354 7.2 Properties of Radicals.........................................365 7.3 Operations of Radicals........................................372 7.4 Radical Equations...............................................382 7.5 Graph of Radical Function..................................388 7.6 Rational and Real Exponents...............................392 8. Exponential and Logarithm 8.1 Composite Function...........................................406 8.2 Inverse Function.................................................410 8.3 Exponential Function..........................................420 8.4 Definition of Logarithms.....................................426 8.5 Laws of Logarithms............................................435 8.6 Log and Exp Equations.......................................443 8.7 The Natural Logarithm Function..........................451 8.8 Exponential Growth and Modeling.......................459 9. Sequence and Series 9.1 Sequence and Series..........................................466 9.2 Arithmetic Sequence and Series..........................475 9.3 Geometric Sequence and Series..........................482 9.4 Infinite Geometric Series....................................488 10. Coordinate Geometry 10.1 Distance and midpoint Formulas.......................496 10.2 Equation of Circle.............................................501 10.3 Basics of Conic Sections...................................510 11. Basic Statistics 11.1 Measuring Center of Data.................................522 11.2 Measuring Spread of Data................................531 11.3 Probability.......................................................541 11.4 Independent and dependent Event....................549 Answers...................................................................559