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Exponential Functions

Theory

the exponential story

Basic Forms

base e

Algebra

exponential form

Logarithmic Functions

Theory

the logarithmic story

Polynomial Functions

Theory

the polynomial story

Factoring

Rational Roots Theorem

FTA

Fundamental Theory of Algebra

Rational Functions

Theory

the rational story

Function Forms

Categories

elementary library

Operations

new functions from old

Pieces

piecewise defined

Composition

step by step

Composition

Steps

range to domain

Formulas

functions

Behavior

increasing and decreasing

Analysis

8 characteristics

More Analysis

8 characteristics

Function Type

the Derivative

Refining

open interval

Algebra

positive and negative

Critical Numbers+

candidates for change

Analysis

8 characteristics

Analyzing Functions

Analyzing

Analyzing

describe everything

Analyzing More Functions

Analyzing

describe everything

Analyzing

describe everything

Quadratic Functions

Theory

iRoC

rate of change

Missing Numbers

need more numbers

2D Numbers

Real Numbers

dots and arrows

Vectors

algebraic geometry

Numbers

2D

Complex Numbers

Notation

Complex Arithmetic

Operations

addition and subtraction

Complex Multiplication

products

Complex Fractions

Fractions

complex quotients

Algebraic Geometry

Polar Form

locating numbers

Direction Vectors

unit vectors

The Unit Circle

The Key

circles and triangles

Right Triangles

Similarity

unit circle again

Side Lengths

Pythagorean Theorem

Angles

inverses

3 Views

information

General Triangles

Law of Sines

proportionalities

Law of Cosine

extending Pythagorus

Trig Functions

Sine & Cosine

Tangent

quotient

Around the Circle

Easy Angles

As Input

composition

Cartesian Graphs

Transform

Polar Graphs

Graphing

polar coordinates

Gallery

polar curves

Rate Of Change

Infinitesimal

notation

Sine and Cosine

More Trig Functions

Cotangent

characteristics

Secant

features

Cosecant

attributes

Inverse Trig Functions

Inverse Functions

one-to-one

Exponential

exponential and logarithmic

ArcSine & ArcCosine

restricting the domain

Arctangent

useful

Complex Bridge

Euler’s Formula

Bridge

exp, trig, hyp

Trig Identities

double and half

Function Analysis

Analyzing

describe everything

Analyzing

describe everything

More Zeros

Quadratic

Pairs

conjugate roots

Reals

linear and quadratic

Rationals

RRT

FTA

Fundamental Theorem of Algebra

More Function Analysis

Analyzing

describe everything

Implicit Functions

Implicit Functions

Rate of Change

no formula

Modeling

Length

rate, length, and time

Angles

elevation and depression

Volume

cubic units

Periodic

tides

Model Analysis

C&M Trucking

least cost

Sequences

Sequences

list functions

Visualize

graphs

Sequences as functions

Limits of Sequences

convergence

Dominant Terms

evaluating limits

Existence

convergence vs. divergence

Sums of sequences

What is a series

adding a sequence

Special Series

geometric

Geometric Series

The Series

formula and domain

Convergence Intervals

center

Closed Form

center

Rational Functions

series

Complex Exponentials

Roots of Unity

unit circle

Roots

roots of complex

Powers

fractional powers

Complex Logarithm

Inverse

too many directions now

Complex Powers

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