# Functions

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Functions

## 1. Sets

### 1.1. Subsets

1.1.1. Interval Notation

1.1.1.1. ( most negative #, most postive # )

1.1.1.2. Bounded

1.1.1.2.1. [3,1)

1.1.1.3. Unbounded

1.1.1.3.1. (3,infinty)

1.1.2. Limit Notation

1.1.2.1. End Behavior

1.1.2.2. Continuity

1.1.2.2.1. Continuous

1.1.2.2.2. Discountinuous

1.1.3. Set Builder Notation

1.1.3.1. {variable | describe properties of #s , ID the # set}

1.1.4. Set Notation

1.1.4.1. ( most negative #, most postive # )

### 1.2. Universal Set

1.2.1. unions

1.2.2. intersections

1.2.3. empty

## 2. Combinations and Compositions

### 2.1. Arithmetic Combinations

2.1.1. f(g(x))

2.1.2. (f - g)(x)

2.1.3. (f + g)(x)

2.1.4. (f/g)(x)

2.1.5. g(f(x))

2.1.6. (f * g)(x)

## 3. Characterizing Functions

### 3.1. Intervals of Functions

3.1.1. Constant

3.1.2. Increasing

3.1.3. Decreasing

3.1.4. Odd /Even/ Neither

3.1.4.1. Algebraic test

3.1.4.1.1. Even F(-x)= F(x)

3.1.4.1.2. Odd F(-x)=-F(x)

3.1.4.2. Type of function

3.1.5. Extrema

3.1.5.1. Relative

3.1.5.2. Absolute

3.2.1. x -axis

3.2.2. y - axis

3.2.3. orgin

### 3.3. Range

3.3.1. All possible y values in a function

### 3.4. Zeros

3.4.1. What is x when y=0?

3.4.1.1. Look in charts to see when y changes from (+) to (-)

### 3.5. y-intercept

3.5.1. What is y when x=0?

3.5.1.1. Plug 0 into x and solve

### 3.6. Parent Functions

3.6.1. Reciprocal

3.6.1.1. f(x)=1/x

3.6.2. Square Root

3.6.2.1. f(x)=√x

3.6.3. Cubic

3.6.3.1. f(x)=x^3

3.6.4.1. f(x)=x^2

3.6.5. Identity

3.6.5.1. f(x)=x

3.6.6. Constant

3.6.6.1. f(x)=c

3.6.7. Step

3.6.7.1. f(x)={[x]}

### 3.8. Domain

3.8.1. All possible x values in a function