Definitions

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Appendix B Definitions

1.1 What is a function?

Definition 1.1.1 Sets and set membership

Definition 1.1.3 Function

Definition 1.1.8 Principal square root function

Definition 1.1.11 Subsets

Definition 1.1.12 Set-builder notation

Definition 1.1.17 Set union and intersection

Definition 1.1.19 Important sets

Definition 1.1.22 Range

Definition 1.1.27 Cartesian plane

Definition 1.1.28 Graph of a function

Definition 1.1.34 Graph of equation

1.2 Linear and quadratic functions

Definition 1.2.2 Linear functions

Definition 1.2.5 Identity function and constant functions

Definition 1.2.6 Quadratic function

Definition 1.2.15 Properties of functions

Definition 1.2.19 Equations of lines

1.3 Modeling with Linear and Quadratic Functions

Definition 1.3.2 Average rate of change

Definition 1.3.20 Cost function

Definition 1.3.23 Revenue Function

Definition 1.3.26 Profit function

1.4 Algebraic functions

Definition 1.4.1 Rational numbers

Definition 1.4.2 Power functions: rational power

Definition 1.4.11 Polynomials

Definition 1.4.19 Rational function

1.5 Algebraic functions: continued

Definition 1.5.24 Function equality

1.6 Transformations and symmetry

Definition 1.6.24 Even and odd functions

1.7 Function composition

Definition 1.7.3 Function composition

1.10 Piecewise-defined functions and absolute value

Definition 1.10.1 Sign function

Definition 1.10.8 Absolute value (geometric)

Definition 1.10.11 Absolute value (piecewise)

Definition 1.10.18 Distance function on \(\R\)

1.11 Introduction to limits

Definition 1.11.3 Limit (informal)

Definition 1.11.12 One-sided limits: informal

Definition 1.11.16 Limit at endpoints of domain

1.14 Limits: formal definition

Definition 1.14.1 Limit (formal)

1.15 Continuity

Definition 1.15.1 Interior points and endpoints

Definition 1.15.2 Continuity

1.16 Limits at infinity

Definition 1.16.1 Limits at infinity

Definition 1.16.5 Horizontal asymptote

1.17 Infinite limits

Definition 1.17.1 Infinite limits (informal)

Definition 1.17.4 Vertical asymptote

1.18 Derivative: at a point

Definition 1.18.1 Derivative at a point

Definition 1.18.5 Difference quotient

Definition 1.18.6 Derivative interpretations

1.19 Derivative: function

Definition 1.19.1 Derivative function

Definition 1.19.8 Leibniz notation

1.20 Derivative: rules

Definition 1.20.11 Higher order derivatives

1.21 Derivative as rate of change

Definition 1.21.3

Definition 1.21.5 Marginal cost, revenue, profit

2.1 Extreme value theorem

Definition 2.1.6 Extreme values

Definition 2.1.12 Critical point

2.3 Linearization

Definition 2.3.2 Linearization of a function

2.4 Monotonicity and first derivative test

Definition 2.4.1 Increasing, decreasing, monotonic

2.5 Concavity and inflection points

Definition 2.5.3 Concavity and inflection points

2.8 Exponential functions

Definition 2.8.2 Exponential Functions