Алгебра. Учебник для 9 кл. с углубл. изучен. математики_Виленкин Н.Я., Сурвилло Г.С. и др_2006 -368с
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Сурвилло Г.С.
Виленкин Н.Я.
Виленкин
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Алгебра. Учебник для 9 кл. с углубл. изучен. математики_Виленкин Н.Я., Сурвилло Г.С. и др_2006 -368с
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Entries
118
Chapter VIII. Functions
Theory
Page 3
Functions. Ways of defining functions
Theory
Page 3
Variable quantities
Theory
Page 3
Concept of a function
Theory
Page 5
Graph of a function
Theory
Page 9
Ways of defining a function
Theory
Page 11
Piecewise definition of a function
Theory
Page 16
Graphs of elementary functions
Theory
Page 17
Linear function
Theory
Page 17
Linear inequalities with two variables
Theory
Page 18
Absolute value function of x
Theory
Page 22
Integer part function
Theory
Page 25
Fractional part function
Theory
Page 26
Sign function sgn x
Theory
Page 27
Functions x^2, 1/x, k/x and their graphs
Theory
Page 29
Function x^2
Theory
Page 29
Functions 1/x and k/x
Theory
Page 32
Transformations of graphs
Theory
Page 34
Parallel translation, graph shift
Theory
Page 35
Stretching and compressing a graph along the Oy axis
Theory
Page 36
Stretching and compressing a graph along the Ox axis
Theory
Page 38
Graphs of functions containing the absolute value sign
Theory
Page 39
Quadratic function and its graph
Theory
Page 41
Quadratic function
Theory
Page 41
Roots of a quadratic function. Common points of a parabola and a line
Theory
Page 45
Dependence of properties of the quadratic function x^2 + px + q on coefficients p and q
Theory
Page 48
Examples of dependencies expressed by a quadratic function
Theory
Page 53
Fractional-linear function and its graph
Theory
Page 54
General properties of functions and graph construction
Theory
Page 58
Even and odd functions
Theory
Page 58
Increasing and decreasing functions
Theory
Page 62
Maximum and minimum points. Greatest and least values of a function on an interval
Theory
Page 68
Reading graphs of functions
Theory
Page 78
Investigating some rational functions and constructing their graphs
Theory
Page 79
Graph of the function 1/f
Theory
Page 86
Applying properties of a quadratic function to problems on finding greatest and least values
Theory
Page 89
Concept of simple mathematical models. Functions in economics
Theory
Page 92
Additional exercises for Chapter VIII
Problem
Page 95
Chapter IX. Powers and roots
Theory
Page 98
Powers and the power function
Theory
Page 98
Powers with integer exponents
Theory
Page 98
Power function
Theory
Page 103
Roots and powers with rational exponents
Theory
Page 107
Roots with natural exponents
Theory
Page 107
Extracting odd-degree roots from negative numbers
Theory
Page 110
Properties of roots of nonnegative numbers
Theory
Page 113
Graph of the nth root function of x
Theory
Page 117
Powers with rational exponents
Theory
Page 120
Powers with rational exponents and production functions in economics
Theory
Page 127
Production function
Theory
Page 127
Cobb—Douglas production function
Theory
Page 128
Isoquants — lines of equal output
Theory
Page 130
Isocosts — lines of equal cost
Theory
Page 132
Minimum firm costs for acquiring resources at a given production volume
Theory
Page 134
Additional exercises for Chapter IX
Problem
Page 139
Chapter X. Equations, inequalities and their systems
Theory
Page 143
Division of polynomials. Roots of polynomials
Theory
Page 143
Division of a polynomial by a polynomial with remainder
Theory
Page 143
Bezout's theorem. Roots of a polynomial. Horner's scheme
Theory
Page 147
Greatest common divisor and least common multiple of polynomials. Euclidean algorithm
Theory
Page 153
Equations with one variable
Theory
Page 156
Basic definitions
Theory
Page 156
Equivalent equations. Consequences of equations
Theory
Page 158
Integral rational equations
Theory
Page 162
Basic methods for solving integral rational equations
Theory
Page 164
Vieta's formulas for higher-degree equations
Theory
Page 176
Fractional-rational equations
Theory
Page 180
Systems of equations with two variables
Theory
Page 184
Basic definitions and methods for solving systems of equations
Theory
Page 184
Equations and systems of equations with parameters
Theory
Page 191
Rational inequalities
Theory
Page 194
Basic definitions
Theory
Page 194
Solving integral rational inequalities. Interval method
Theory
Page 196
Solving fractional-rational inequalities
Theory
Page 198
Proving inequalities
Theory
Page 201
Irrational equations and inequalities
Theory
Page 204
Irrational equations
Theory
Page 204
Irrational inequalities
Theory
Page 209
Graphical solution of inequalities and systems of inequalities with two unknowns
Theory
Page 215
Systems of equations and market equilibrium
Theory
Page 218
Additional exercises for Chapter X
Problem
Page 225
Chapter XI. Sequences
Theory
Page 233
Numerical sequences
Theory
Page 233
Method of mathematical induction
Theory
Page 239
Arithmetic progression
Theory
Page 245
Definition of an arithmetic progression
Theory
Page 245
Sum of the first n terms of an arithmetic progression
Theory
Page 248
Geometric progression
Theory
Page 251
Definition of a geometric progression
Theory
Page 251
Sum of the first n terms of a geometric progression
Theory
Page 256
Limit of a sequence
Theory
Page 259
Definition of an infinitesimal sequence
Theory
Page 259
Properties of infinitesimal sequences
Theory
Page 262
Infinitely large sequences
Theory
Page 265
Definition of the limit of a sequence
Theory
Page 266
Theorems on limits
Theory
Page 269
Criterion for the existence of a limit. Calculating limits of recursively defined sequences
Theory
Page 272
Sequences of sums. Sum of an infinite decreasing geometric progression
Theory
Page 275
Progressions, percentages and banking calculations
Theory
Page 279
What is a bank
Theory
Page 279
Arithmetic progression and simple interest
Theory
Page 280
Geometric progression and compound interest
Theory
Page 282
Simple model of a banking system
Theory
Page 284
Additional exercises for Chapter XI
Problem
Page 288
Chapter XII. Elements of combinatorics and probability theory
Theory
Page 295
Basic concepts of combinatorics
Theory
Page 295
Sum rule and product rule
Theory
Page 296
Arrangements
Theory
Page 299
Permutations
Theory
Page 302
Combinations
Theory
Page 304
Concept of probability of an event
Theory
Page 308
Introduction
Theory
Page 308
Frequency and probability. Statistical definition of event probability
Theory
Page 309
Experiments with a finite number of equally likely outcomes
Theory
Page 314
Outcomes and events
Theory
Page 317
Calculating probabilities in experiments with equally likely outcomes, classical approach
Theory
Page 318
Operations on events and algebraic operations with probabilities
Theory
Page 326
Answers
Answer
Page 346
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