Cover
Title Page
Copyright Page
Contents
Introduction
1 Functions: An introduction
Relations and inverses
Functions
Function notation
Arithmetic of functions
Transformation of functions
Inverse of a function
Graphical representation of functions
2 Linear equations and inequalities
Simple linear equations
System of linear equations—graphical
System of linear equations—substitution
System of linear equations—elimination
System of linear equations—three variables
System of linear equations—matrix
System of linear equations—application
Linear inequalities
System of linear inequalities
Absolute value equations
Absolute value inequalities
3 Quadratic relationships
The parabola
Special factoring formulas
Trial and error
Completing the square
Quadratic formula
Applications
Square root function
Circles
Ellipses
Hyperbolas
Systems of equations
4 Complex numbers
Powers of i
Arithmetic of complex numbers
The discriminant and nature of the roots of a quadratic equation
Sum and product of roots of a quadratic equation
5 Polynomial functions
Even and odd functions
Inverse functions
End behavior
Factor theorem
6 Rational and irrational functions
Rational functions
Multiplying and dividing rational expressions
Adding and subtracting rational expressions
Solving rational equations
Irrational functions
Simplifying irrational expressions
Solving irrational equations
7 Exponential and logarithmic functions
Properties of exponents
Exponential and logarithmic functions
Properties of logarithms
Solving exponential and logarithmic equations
8 Sequences and series
Summation notation
Recursion
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
9 Introduction to probability
Fundamental theorem of counting
Permutations
Combinations
Binomial expansions
Conditional probability
Binomial probability/Bernoulli trial
10 Introduction to statistics
Measures of central tendency
Measures of dispersion
Normal distribution
Regressions
11 Inferential statistics
Basics
Central limit theorem and standard error
Standardized (z) scores
The basics of inferential statistics
Confidence intervals
Tests of hypotheses
Simulation
12 Trigonometry: Right triangles and radian measure
Right triangle trigonometry
Special right triangles
The unit circle: First quadrant
The unit circle—beyond the first quadrant
Radian measure
Basic trigonometric identities
Area of a triangle
Law of sines
Ambiguous case
Law of cosines
13 Graphs of trigonometric functions
Amplitude and period
Graphing trigonometric functions
Inverse trigonometric functions
Solving trigonometric equations
Answer key