Table of Contents
Introduction ix
1 Functions: An introduction 1
Relations and inverses 1
Functions 2
Function notation 3
Arithmetic of functions 4
Transformation of functions 6
Inverse of a function 9
Graphical representation of functions 10
2 Linear equations and inequalities 15
Simple linear equations 15
System of linear equations-graphical 18
System of linear equations-substitution 20
System of linear equations-elimination 21
System of linear equations-three variables 23
System of linear equations-matrix 25
System of linear equations-application 27
Linear inequalities 30
System of linear inequalities 31
Absolute value equations 35
Absolute value inequalities 36
3 Quadratic relationships 38
The parabola 38
Special factoring formulas 41
Trial and error 42
Completing the square 47
Quadratic formula 48
Applications 50
Square root function 52
Circles 53
Ellipses 54
Hyperbolas 56
Systems of equations 59
4 Complex numbers 62
Powers of i 62
Arithmetic of complex numbers 63
The discriminant and nature of the roots of a quadratic equation 65
Sum and product of roots of a quadratic equation 67
5 Polynomial functions 69
Even and odd functions 69
Inverse functions 71
End behavior 72
Factor theorem 73
6 Rational and irrational functions 75
Rational functions 75
Multiplying and dividing rational expressions 77
Adding and subtracting rational expressions 79
Solving rational equations 82
Irrational functions 84
Simplifying irrational expressions 85
Solving irrational equations 86
7 Exponential and logarithmic functions 89
Properties of exponents 89
Exponential and logarithmic functions 92
Properties of logarithms 95
Solving exponential and logarithmic equations 97
8 Sequences and series 103
Summation notation 103
Recursion 104
Arithmetic sequences 106
Arithmetic series 107
Geometric sequences 108
Geometric series 110
9 Introduction to probability 112
Fundamental theorem of counting 112
Permutations 114
Combinations 116
Binomial expansions 118
Conditional probability 120
Binomial probability/Bernoulli trial 123
10 Introduction to statistics 126
Measures of central tendency 126
Measures of dispersion 129
Normal distribution 134
Regressions 141
11 Inferential statistics 149
Basics 149
Central limit theorem and standard error 150
Standardized (z) scores 153
The basics of inferential statistics 155
Confidence intervals 156
Tests of hypotheses 159
Simulation 162
12 Trigonometry: Right triangles and radian measure 166
Right triangle trigonometry 166
Special right triangles 169
The unit circle: First quadrant 170
The unit circle-beyond the first quadrant 172
Radian measure 174
Basic trigonometric identities 176
Area of a triangle 179
Law of sines 180
Ambiguous case 182
Law of cosines 185
13 Graphs of trigonometric functions 189
Amplitude and period 189
Graphing trigonometric functions 191
Inverse trigonometric functions 195
Solving trigonometric equations 199
Answer key 202
