# Functions

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Functions by

## 2. Sets

### 2.1. Reals

2.1.1. Rational

2.1.1.1. Integers

2.1.1.2. Wholes

2.1.1.3. Naturals

2.1.2. Irrational

### 2.2. Universal set

2.2.1. Unions

2.2.1.1. U

2.2.1.2. "or"

2.2.2. Intersections

2.2.2.1. "and"

2.2.2.2. ∩

2.2.3. Empty Set

## 3. Notation

### 3.1. Interval

3.1.1. Unbounded

3.1.2. bounded

3.1.3. inequalities

### 3.2. Function Notation

3.2.1. Independent Variable

3.2.2. Dependent Variable

### 3.3. Set-builder

3.3.1. properties

## 4. Behavior

### 4.1. End Behavior

4.1.1. Right End

4.1.1.1. lim f(x)

4.1.2. Left End

4.1.2.1. lim f(x)

4.2.1. Minimum

4.2.2. Maximum

## 5. Graphing

### 5.1. Symmetry

5.1.1. Origin

5.1.1.1. ODD

5.1.2. Point Symmetry

5.1.3. Line Symmetry

5.1.4. Y-axis

5.1.4.1. EVEN

5.1.5. X-axis

### 5.2. Range

5.2.1. Y-intercept

### 5.3. Domain

5.3.1. Implied

5.3.2. Relevent

5.3.3. X-intercept

5.3.3.1. Zeros

5.3.3.1.1. Roots

### 5.4. Average Rate of Change

5.4.1. Secant line

5.4.2. Average Rate of Change Formula

## 6. Continuity Test

6.1.1. Limit

### 6.2. Discontinuous

6.2.1. Removable

6.2.2. Nonremovable

6.2.2.1. Jump

6.2.2.2. Infinite

## 7. Parent Functions

### 7.1. f(x)=/x/

7.1.1. Absolute Value

### 7.2. f(x)=C

7.2.1. Constant Function

7.2.2. Zero Function

### 7.3. f(x)=x

7.3.1. Identity Function

### 7.5. f(x)=x^3

7.5.1. (picture Here)

7.5.2. Cubic Function

### 7.6. f(x) = 1/x

7.6.1. Reciprocal Function

### 7.7. f(x) = √x

7.7.1. (picture here)

7.7.2. Square Root Function

### 7.8. Inverse

7.8.1. f(g(x))

7.8.1.1. (fog)(x)

7.8.2. Every domain has one corresponding range and every range has one corresponding domain.

7.8.2.1. one to one

7.8.3. f^-1(x)

7.8.4. Is It's own inverse

7.8.5. Inverse is not a function as it stands.

### 7.9. Transformations

7.9.1. Dilations

7.9.1.1. Horizontal Compression

7.9.1.1.1. g(x)= f(ax); a>1

7.9.1.2. Horizontal Stretch

7.9.1.2.1. g(x)= f(ax); 0<a<1

7.9.1.3. Vertical Stretch

7.9.1.3.1. g(x)= af(x); a>1

7.9.1.4. Vertical Compression

7.9.1.4.1. g(x)= af(x); 0<a<1

7.9.2. Reflections

7.9.2.1. Over Y-axis

7.9.2.1.1. g(x)= -f(x)

7.9.2.2. Over X-axis

7.9.2.2.1. g(x)- f(-x)

7.9.3. Translations

7.9.3.1. Vertical

7.9.3.1.1. Up

7.9.3.1.2. Down

7.9.3.2. Horizontal

7.9.3.2.1. Left

7.9.3.2.2. Right