Introduction to Graphs and Graphers 

1  (20) 
Basic Concepts of Algebra 



20  (5) 

Integer Exponents, Scientific Notation, and Order of Operations 


25  (7) 

Addition, Subtraction, and Multiplication of Polynomials 


32  (4) 


36  (4) 


40  (9) 

Radical Notation and Rational Exponents 


49  (9) 


58  (8) 


66  (6) 

Modeling and Applications 


72  (12) 


79  (5) 

Graphs, Functions, and Models 



Functions, Graphs, and Graphers 


84  (14) 

Functions and Applications 


98  (13) 

Linear Functions and Applications 


111  (16) 

Data Analysis, Curve Fitting, and Linear Regression 


127  (8) 

Distance, Midpoints, and Circles 


135  (5) 


140  (7) 

Transformations of Functions 


147  (11) 


158  (14) 


167  (5) 

Polynomial and Rational Functions 



Introduction to Polynomial Functions and Complex Numbers 


172  (8) 

Quadratic Equations and Functions 


180  (16) 

Polynomial Models and Curve Fitting 


196  (12) 

Polynomial Division; The Remainder and Factor Theorems 


208  (7) 

Theorems about OSPF Zeros of Polynomial Functions 


215  (9) 


224  (14) 

Polynomial and Rational Inequalities 


238  (12) 


245  (5) 

Exponential and Logarithmic Functions 




250  (11) 

Exponential Functions and Graphs 


261  (13) 

Logarithmic Functions and Graphs 


274  (13) 

Properties of Logarithmic Functions 


287  (9) 

Solving Exponential and Logarithmic Equations 


296  (7) 

Applications and Models: Growth and Decay 


303  (19) 


318  (4) 

The Trigonometric Functions 



Trigonometric Functions of Acute Angles 


322  (11) 

Applications of Right Triangles 


333  (10) 

Trigonometric Functions of Any Angle 


343  (15) 

Radians, Arc Length, and Angular Speed 


358  (14) 

Circular Functions: Graphs and Properties 


372  (17) 

Graphs of Transformed Sine and Cosine Functions 


389  (21) 


404  (6) 

Trigonometric Identities, Inverse Functions, and Equations 



Identities: Pythagorean and Sum and Difference 


410  (13) 

Identities: Cofunction, DoubleAngle, and HalfAngle 


423  (8) 

Proving Trigonometric Identities 


431  (7) 

Inverses of the Trigonometric Functions 


438  (10) 

Solving Trigonometric Equations 


448  (16) 


459  (5) 

Applications of Trigonometry 




464  (12) 


476  (8) 

Complex Numbers: Trigonometric Form 


484  (12) 

Polar Coordinates and Graphs 


496  (9) 


505  (17) 


518  (4) 



Systems of Equations in Two Variables 


522  (10) 

Systems of Equations in Three or More Variables 


532  (8) 

Matrices and Systems of Equations 


540  (8) 


548  (12) 


560  (6) 

Systems of Inequalities and Linear Programming 


566  (11) 


577  (13) 


585  (5) 




590  (8) 

The Circle and the Ellipse 


598  (10) 


608  (9) 

Nonlinear Systems of Equations 


617  (13) 


625  (5) 

Sequences, Series, and Combinatorics 




630  (11) 

Artithmetic Sequences and Series 


641  (10) 

Geometric Sequences and Series 


651  (11) 


662  (7) 

Combinatorics: Permutations 


669  (10) 

Combinatorics: Combinations 


679  (7) 


686  (9) 


695  (14) 


705  (4) 
Appendixes 

709  

A Determinants and Cramer's Rule 


709  


716  
Answers 

A1  
Index of Applications 

I1  
Index 

I5  