CSCC PreCalculus 1

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Relations

A Package

information packages

Functions

What is a Function?

one additional rule

Reading and Writing

language

Function Properties

characteristics, features

Number Functions

measurements

Real-Valued

Set Symbols

vocabulary

Subsets of Real Numbers

intervals

Endpoints

dots

Open Sets

always room

Real-Valued Functions

connecting reals

∞

not a number

Function Graphs

Encoding Visually

pairs to dots

Decoding Visually

dots to pairs

Function Features

extreme values

Function Behavior

relative change

Formulas

The Formula Tool

part 1

The Formula Tool

part 2

Formulas and Graphs

bridge

Parentheses

grouping

Piecewise Functions

Stitching Functions

pieces and parts

Famous Piecewise

examples

Periodic Functions

repeating

Recursive Functions

formula of formulas

Graphical Language

Graph Symbols

communication

Inaccurate

suspicious

Counter Examples

dealing with all

Visual Features

Domain

inputs

Zeros

intercepts

Discontinuity

sudden breaks

End-Behavior

settling down

Visual Behavior

Change

increasing and decreasing

Optimization

minimum and maximum

Analysis

rigor

Proportional Change

Change

regular

Linear Forms

constant rate

Lines

slope

Accumulation

adding rates

Systems

intersection

Analysis

8 characteristics

Projectile Motion

Gravity

inverse square law

Quadratic Forms

complete the square

Quadratic Zeros

quadratic formula

Quadratic Forms

vertex form

Quadratic Products

factoring

Parabolas

quadratic graphs

Quadratic Behavior

Tangent Lines

zooming in

Tangents

intervals to points

Quadratic Analysis

behavior

Two Sides

both sides together

One Side

each side separate

Piecewise Analysis

Analyzing

characteristics and features

Piecewise Evaluation

selecting formulas

Piecewise Intersection

equations

Elementary Library 1

Polynomials

sums of power functions

Rational

fractions of polynomials

Roots and Radicals

separating dimensions

Categories

templates

Elementary Library 2

Exponential

percentage growth

Logarithmic

reverse

Trigonometric

sine and cosine

Absolute Value

distance

Categories

Templates

Shifting

Shifting Domain

same characteristics

Left and Right

sliding the graph

Shifting Range

same characteristics

Up and Down

sliding the graph

Library Analysis 1

Polynomials

characteristics

Rational

features

Roots and Radicals

aspects

Categories

forms

Library Analysis 2

Exponential

attributes

Shifted Exponential

aspects

Logarithmic

inverse

Trigonometric

facets

Absolute Value

traits

Categories

forms

Pointwise Composition

Output Is Input

evaluating

Piecewise Functions

output $\rightarrow$ input

Stretching

Left and Right

stretch the domain

Up and Down

stretch the range

Transform

shape

Just the Algebra

Piecewise Composition

Linear Composition

linear linear linear

Piecewise Functions

piecewise linear

More Pieces

piecewise linear

Percent Change

Growth Rates

constant percentage

Exponential Functions

characteristics

Shifted Exponential

shifted range

Logarithmic Functions

exponents

Composed

reversed functions

Exponential Algebra

Exponential Rules

rules

Logarithmic Rules

rules

Function Values

expected values

Broken Values

“should be” values

Missing Values

blink

Limits

language of behavior

Space

surrounding values

Open Intervals

always space

Closeness

relative distance

Endpoints

intersection

Continuity

Discontinuity

breaks

Singularity

holes

Continuity

close as you want

Elementary Functions

nice

Function Behavior

End Behavior

approaching infinity

Limiting Behavior

limit notation

Comparing Functions

Dominance

bigger faster

Indeterminate

equally fast

Rate Of Change

Function of Change

rate as a relationship

Comparing

Mean Value Theorem

Function Zeros

Zero Property

factoring

Solving Equations

break it up

Solving Inequalities

still break up

Rate of Change

critical numbers

Equivalent Forms

Alternate Formulas

many representations

Equivalent Enough

watching the domain

Approximate Behavior

Approximating Functions

tangent lines

Accumulation

rates over time

Transform the Inside

Inside

domain

Graph Movement

horizontal

Transform the Outside

Outside

range

Graph Movement

vertical

All Together

range

Composition

Assemble

putting functions together

Algebraically

replacing

Disassemble

taking apart

Rate for Composition

rates of rates

Function Algebra

A New Operation

Inverse Functions

one-to-one

Exponential

exponential and logarithmic

Trigonometric

coordinates to angles

Function Analysis

Describe Everything

characteristics

Describe Everything

features