# Functions

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Functions

## 2. Characteristics

### 2.1. Intercepts

2.1.1. Y-Intercrepts

2.1.2. Zeros (X-intercepts)

2.2.1. Relative

2.2.1.1. Min

2.2.1.2. Max

2.2.2. Absolute

2.2.2.1. Max

2.2.2.2. Min

2.4.1. origin

2.4.1.1. neither

2.4.2. x-axis

2.4.2.1. even

2.4.3. y-axis

2.4.3.1. odd

## 3. Sets

### 3.4. Number groups

3.4.1. real

3.4.1.1. rational

3.4.1.1.1. integers

3.4.1.2. irrational

### 3.5. Universal Set

3.5.1. All numbers possible within a given example

## 4. graphs

### 4.1. Transformations

4.1.1. Translations

4.1.1.1. Vertical

4.1.1.2. Horizontal

4.1.2. Dilations

4.1.2.1. Vertical Compression

4.1.2.1.1. Change in y values

4.1.2.2. Vertical stretch

4.1.2.2.1. change in y values

4.1.2.3. Horizontal Compression

4.1.2.3.1. Change in x values

4.1.2.4. Horizontal Stretch

4.1.2.4.1. Change in x values

4.1.3. Reflection

4.1.3.1. over x-axis

4.1.3.2. over y axis

4.1.4. Absolute Value

4.1.4.1. f(x)=lxl+5

4.1.4.2. f(x)=lx+5l

### 4.2. Parent Functions

4.2.1. Identity

4.2.2. Cubic

4.2.4. Constant

4.2.5. Square root

4.2.6. Reciprocal function

4.2.7. Absolute Value

4.2.8. Greatest Integer

## 5. Equations

### 5.1. Average Rate of Change

5.1.1. Secant Line

### 5.2. Range

5.2.1. Interval Notation

5.2.2. Set-Builder Notation

### 5.3. Domain

5.3.1. Interval Notation

5.3.2. Set-Builder Notation

### 5.4. Operations on Functions

5.4.2. Subtraction

5.4.3. Multiplication

5.4.4. Division

### 5.5. Compositions of Functions

5.5.1. Real World Applications

5.5.2. Examples

5.5.2.1. (g o f)(x)

5.5.2.1.1. (g/f)(x)

5.5.2.2. (f o g)(x)

5.5.2.2.1. (f/g)(x)

5.5.3. Determining if functions have inverses.

### 5.6. Inverses

5.6.1. Flip x and y to find inverse.

5.6.2. (f o g)(x) and (g o f)(x) should both equal x

5.6.3. Domain and Range flips

5.6.4. coordinates reflect over the line f(x)=x

5.6.5. Notated f^-1(x)=x

### 5.7. Factoring

5.7.1. GCF

5.7.1.1. 4 terms

5.7.1.2. Perfect Squares

5.7.1.3. Coefficient of 1

5.7.1.4. Coefficient of Greater than 1

## 6. Limits

### 6.1. Limit Notation

6.1.1. End Behavior

## 7. Continuity

### 7.1. Continuity Test

7.1.1. Continuous

7.1.1.1. lim f(x) as x approaches limit= f(x)

7.1.2. Discontinuous

7.1.2.1. removable

7.1.2.2. non removable

7.1.2.2.1. infinite

7.1.2.2.2. jump