- Chapter 1.1: Graphs and Graphing Utilities
- Chapter 1.10: Modeling with Functions
- Chapter 1.2: Basics of Functions and Their Graphs
- Chapter 1.3: More on Functions and Their Graphs
- Chapter 1.4: Linear Functions and Slope
- Chapter 1.5: More on Slope
- Chapter 1.6: Transformations of Functions
- Chapter 1.7: Combinations of Functions; Composite Functions
- Chapter 1.8: Inverse Functions
- Chapter 1.9: Distance and Midpoint Formulas; Circles
- Chapter 10.1: Sequences and Summation Notation
- Chapter 10.2: Arithmetic Sequences
- Chapter 10.3: Geometric Sequences and Series
- Chapter 10.4: Mathematical Induction
- Chapter 10.5: The Binomial Theorem
- Chapter 10.6: Counting Principles, Permutations, and Combinations
- Chapter 10.7: Probability
- Chapter 11.1: Finding Limits Using Tables and Graphs
- Chapter 11.2: Finding Limits Using Properties of Limits
- Chapter 11.3: Limits and Continuity
- Chapter 11.4: Introduction to Derivatives
- Chapter 2.1: Complex Numbers
- Chapter 2.2: Quadratic Functions
- Chapter 2.3: Polynomial Functions and Their Graphs
- Chapter 2.4: Dividing Polynomials; Remainder and Factor Theorems
- Chapter 2.5: Zeros of Polynomial Functions
- Chapter 2.6: Rational Functions and Their Graphs
- Chapter 2.7: Polynomial and Rational Inequalities
- Chapter 2.8: Modeling Using Variation
- Chapter 3.1: Exponential Functions
- Chapter 3.2: Logarithmic Functions
- Chapter 3.3: Properties of Logarithms
- Chapter 3.4: Exponential and Logarithmic Equations
- Chapter 3.5: Exponential Growth and Decay; Modeling Data
- Chapter 4.1: Angles and Radian Measure
- Chapter 4.2: Trigonometric Functions: The Unit Circle
- Chapter 4.3: Right Triangle Trigonometry
- Chapter 4.4: Trigonometric Functions of Any Angle
- Chapter 4.5: Graphs of Sine and Cosine Functions
- Chapter 4.6: Graphs of Other Trigonometric Functions
- Chapter 4.7: Inverse Trigonometric Functions
- Chapter 4.8: Applications of Trigonometric Functions
- Chapter 5.1: Verifying Trigonometric Identities
- Chapter 5.2: Sum and Difference Formulas
- Chapter 5.3: Double-Angle, Power-Reducing, and Half-Angle Formulas
- Chapter 5.4: Product-to-Sum and Sum-to-Product Formulas
- Chapter 5.5: Trigonometric Equations
- Chapter 6.1: The Law of Sines
- Chapter 6.2: The Law of Cosines
- Chapter 6.3: Polar Coordinates
- Chapter 6.4: Graphs of Polar Equations
- Chapter 6.5: Complex Numbers in Polar Form; DeMoivre s Theorem
- Chapter 6.6: Vectors
- Chapter 6.7: The Dot Product
- Chapter 7.1: Systems of Linear Equations in Two Variables
- Chapter 7.2: Systems of Linear Equations in Three Variables
- Chapter 7.3: Partial Fractions
- Chapter 7.4: Systems of Nonlinear Equations in Two Variables
- Chapter 7.5: Systems of Inequalities
- Chapter 7.6: Linear Programming
- Chapter 8.1: Matrix Solutions to Linear Systems
- Chapter 8.2: Inconsistent and Dependent Systems and Their Applications
- Chapter 8.3: Matrix Operations and Their Applications
- Chapter 8.4: Multiplicative Inverses of Matrices and Matrix Equations
- Chapter 8.5: Determinants and Cramer s Rule
- Chapter 9.1: The Ellipse
- Chapter 9.2: The Hyperbola
- Chapter 9.3: The Parabola
- Chapter 9.4: Rotation of Axes
- Chapter 9.5: Parametric Equations
- Chapter 9.6: Conic Sections in Polar Coordinates
- Chapter Chapter 1: Functions and Graphs
- Chapter Chapter 10: Sequences, Induction, and Probability
- Chapter Chapter 11: Introduction to Calculus
- Chapter Chapter 2: Polynomial and Rational Functions
- Chapter Chapter 3: Equations and Inequalities
- Chapter Chapter 4: Trigonometric Functions
- Chapter Chapter 5: Analytic Trigonometry
- Chapter Chapter 6: Additional Topics in Trigonometry
- Chapter Chapter 7: Systems of Equations and Inequalities
- Chapter Chapter 8: Matrices and Determinants
- Chapter Chapter 9: Conic Sections and Analytic Geometry
- Chapter Chapter P: Prerequisites: Fundamental Concepts of Algebra
- Chapter P.1: Algebraic Expressions, Mathematical Models, and Real Numbers
- Chapter P.2: Exponents and Scientific Notation
- Chapter P.3: Radicals and Rational Exponents
- Chapter P.4: Polynomials
- Chapter P.5: Factoring Polynomials
- Chapter P.6: Rational Expressions
- Chapter P.7: Equations
- Chapter P.8: Modeling with Equations
- Chapter P.9: Linear Inequalities and Absolute Value Inequalities
Precalculus 4th Edition - Solutions by Chapter
Full solutions for Precalculus | 4th Edition
Absolute value of a vector
See Magnitude of a vector.
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!
A logarithm with base 10.
Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint
Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
Divisor of a polynomial
See Division algorithm for polynomials.
Matrices that have the same order and equal corresponding elements.
See Equilibrium point.
The terms of the Fibonacci sequence.
The complex number.
Natural exponential function
The function ƒ1x2 = ex.
A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).
See Sequence of partial sums.
The collection of probabilities of outcomes in a sample space assigned by a probability function.
A graph of a polar equation or r = a cos nu.
A square matrix with zero determinant
Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
A shift of a graph up or down.
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