# Functions

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Functions

## 2. Sets & Subsets

### 2.3. Universal

2.3.1. Subset

2.3.2. Unions & Intersections

## 3. Types

### 3.1. Parent Functions

3.1.1. Absolute Value Function

3.1.1.1. |f(x)|

3.1.1.2. f(|x|)

3.1.2. Constant/Zero Function f(x)=C

3.1.3. Identity Function f(x)=x

3.1.4. Quadratic Function f(x)=x^2

3.1.5. Square Root Function f(x)= √x

3.1.6. Cubic Function f(x)=x^3

3.1.7. Reciprocal Function f(x)=1/x

3.1.8. Greatest Integer Function f(x)= [[x]]

### 3.2. Special Functions

3.2.1. piece-wise functions (include boundaries)

3.2.1.1. domain

3.2.1.1.1. x/# set domain =0 ,restrict, use interval notation

3.2.1.1.2. √x+# set greater than or equal to 0

3.2.1.1.3. left to right on graph

3.2.1.2. range

3.2.1.2.1. up and down on graph

## 4. Limits

### 4.1. End behavior

4.1.1. approaching specific values

4.1.2. Extrema

4.1.2.1. Finding Average rate of change

4.1.2.1.1. m sec= f(x)2-f(x)1/ x2-x1

4.1.2.1.2. estimating absolute and relative extrema

4.1.2.2. Analyzing increasing and decreasing behavior/constants

4.1.3. lim f(x)= L as x approaches a certain value

## 5. Transformations

### 5.2. Translations

5.2.1. Vertical

5.2.2. Horizontal

5.3.1. Compress

5.3.2. Strech

## 6. Graphing

### 6.1. Continuity

6.1.1. Testing

6.1.1.1. Continuous

6.1.1.1.1. Table: f(x)lim=f(x) as x approaches c

6.1.1.2. Discontinuous

6.1.1.2.1. Removable

6.1.1.2.2. Infinite

6.1.1.2.3. Jump

### 6.2. Symmetry

6.2.1. X-axis

6.2.2. Y-axis

6.2.3. Origin

6.2.3.1. Even, Odd, or Neither

## 7. Combinations and compositions

### 7.1. Inverses

7.1.1. Horizontal Line Test