CSCC PreCalculus 1

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1Relations

1.1A Package

information packages

2Functions

2.1What is a Function?

one additional rule

2.2Reading and Writing

language

2.3Function Properties

characteristics, features

2.4Number Functions

measurements

3Real-Valued

3.1Set Symbols

vocabulary

3.2Subsets of Real Numbers

intervals

3.3Endpoints

dots

3.4Open Sets

always room

3.5Real-Valued Functions

connecting reals

3.6∞

not a number

4Function Graphs

4.1Encoding Visually

pairs to dots

4.2Decoding Visually

dots to pairs

4.3Function Features

extreme values

4.4Function Behavior

relative change

5Formulas

5.1The Formula Tool

part 1

5.2The Formula Tool

part 2

5.3Formulas and Graphs

bridge

5.4Parentheses

grouping

6Piecewise Functions

6.1Stitching Functions

pieces and parts

6.2Famous Piecewise

examples

6.3Periodic Functions

repeating

6.4Recursive Functions

formula of formulas

7Graphical Language

7.1Graph Symbols

communication

7.2Inaccurate

suspicious

7.3Counter Examples

dealing with all

8Visual Features

8.1Domain

inputs

8.2Zeros

intercepts

8.3Discontinuity

sudden breaks

8.4End-Behavior

settling down

9Visual Behavior

9.1Change

increasing and decreasing

9.2Optimization

minimum and maximum

9.3Analysis

rigor

10Proportional Change

10.1Change

regular

10.2Linear Forms

constant rate

10.3Lines

slope

10.4Accumulation

adding rates

10.5Systems

intersection

10.6Analysis

8 characteristics

11Projectile Motion

11.1Gravity

inverse square law

11.2Quadratic Forms

complete the square

11.3Quadratic Zeros

quadratic formula

11.4Quadratic Forms

vertex form

11.5Quadratic Products

factoring

11.6Parabolas

quadratic graphs

12Quadratic Behavior

12.1Tangent Lines

zooming in

12.2Tangents

intervals to points

12.3Quadratic Analysis

behavior

12.4Two Sides

both sides together

12.5One Side

each side separate

13Piecewise Analysis

13.1Analyzing

characteristics and features

13.2Piecewise Evaluation

selecting formulas

13.3Piecewise Intersection

equations

14Elementary Library 1

14.1Polynomials

sums of power functions

14.2Rational

fractions of polynomials

14.3Roots and Radicals

separating dimensions

14.4Categories

templates

15Elementary Library 2

15.1Exponential

percentage growth

15.2Logarithmic

reverse

15.3Trigonometric

sine and cosine

15.4Absolute Value

distance

15.5Categories

Templates

16Shifting

16.1Shifting Domain

same characteristics

16.2Left and Right

sliding the graph

16.3Shifting Range

same characteristics

16.4Up and Down

sliding the graph

17Library Analysis 1

17.1Polynomials

characteristics

17.2Rational

features

17.3Roots and Radicals

aspects

17.4Categories

forms

18Library Analysis 2

18.1Exponential

attributes

18.2Shifted Exponential

charcateristics

18.3Logarithmic

inverse

18.4Trigonometric

facets

18.5Absolute Value

traits

18.6Categories

forms

18.7Continuity

no breaks

19Pointwise Composition

19.1Output Is Input

evaluating

19.2Piecewise Functions

output $\rightarrow$ input

20Stretching

20.1Left and Right

stretch the domain

20.2Up and Down

stretch the range

20.3Transform

shape

20.4Just the Algebra

no pictures

21Piecewise Composition

21.1Linear Composition

linear linear linear

21.2Piecewise Functions

piecewise linear

21.3More Pieces

piecewise linear

22Percent Change

22.1Growth Rates

constant percentage

22.2Exponential Functions

characteristics

22.3Shifted Exponential

shifted range

22.4Logarithmic Functions

exponents

22.5Composed

reversed functions

23Exponential Algebra

23.1Exponential Rules

rules

23.2Logarithmic Rules

rules

24Function Values

expected values

24.1Broken Values

“should be” values

24.2Missing Values

blink

24.3Limits

language of behavior

25Space

surrounding values

25.1Open Intervals

always space

25.2Closeness

relative distance

25.3Endpoints

intersection

26Continuity

26.1Discontinuity

breaks

26.2Singularity

holes

26.3Continuity

close as you want

26.4Elementary Functions

nice

27Function Behavior

27.1End Behavior

approaching infinity

27.2Limiting Behavior

limit notation

28Comparing Functions

28.1Dominance

relatively bigger

28.2Indeterminate

no dominance

29Rate Of Change

29.1Function of Change

rate as a relationship

29.2Comparing

Mean Value Theorem

29.3Exponential

itself

29.4Logarithmic

reciprocal

30Function Zeros

30.1Zero Property

factoring

30.2Solving Equations

break it up

30.3Solving Inequalities

still break up

30.4Rate of Change

critical numbers

31Equivalent Forms

31.1Alternate Formulas

many representations

31.2Equivalent Enough

domain watching

32Approximate Behavior

32.1Approximating Functions

tangent lines

32.2Accumulation

rates over time

33Transform the Inside

33.1Inside

domain

33.2Graph Movement

horizontal

34Transform the Outside

34.1Outside

range

34.2Graph Movement

vertical

34.3All Together

range

35Composition

35.1Assemble

putting functions together

35.2Algebraically

replacing

35.3Disassemble

taking apart

35.4Rate for Composition

rates of rates

36Function Algebra

36.1A New Operation

composition

36.2Inverse Functions

one-to-one

36.3Exponential

exponential and logarithmic

36.4Trigonometric

coordinates to angles

37Function Analysis

37.1Describe Everything

characteristics

37.2Describe Everything

features