Functions

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Functions

1. Graphing

1.1. Finding Zeros

1.1.1. Finding x-intercepts

1.1.2. Finding y-intercepts

1.2. Extrema

1.2.1. Maximum and Minimum

1.2.1.1. Relative

1.2.1.2. Absolute

1.3. Symmetry

1.3.1. Y-axis Symmetry

1.3.1.1. Even

1.3.2. X-axis Symmetry

1.3.2.1. Not a Function

1.3.3. Origin Symmetry

1.3.3.1. Odd

1.5. Limits

1.5.1. End Behavior

1.5.1.1. Increasing, Decreasing, and Constant

1.5.2. Limit Notation

2. Combinations and Compositions

2.1. Compositions

2.1.1. Algebraically

2.1.2. Graphically

2.1.3. (fog)(x)

2.1.4. Use Unsimplified Version to Find Doman

2.2. Combinations

2.2.1. Algebraically

2.2.2. Graphically

2.2.3. Multiply, Divide, Add, and Subtract Functions

3. Parent Functions

3.1. 8 types

3.1.1. Greatest Integer Function

3.1.2. Absolute Value Function

3.1.3. Constant Function

3.1.4. Idenity Function

3.1.6. Cubic Function

3.1.7. Square Root Function

3.1.8. Reciprocal Function

3.2. Transformation

3.2.1. Translation

3.2.1.1. Up or Down

3.2.1.2. Left or Right

3.2.2. Dialation

3.2.2.1. Horizontal

3.2.2.1.1. Compression

3.2.2.1.2. Stretch

3.2.2.2. Vertical

3.2.2.2.1. Compression

3.2.2.2.2. Stretch

3.2.3. Reflection

3.2.3.1. Over x-axis

3.2.3.2. Over y-axis

3.3. Inverses

3.3.1. Finding

3.3.1.1. Switch Domain and Range

3.3.2. One-to-one

3.3.2.1. Horzontal Line Test

3.3.3. Checking Algebraically

3.3.3.1. Plug One Into the Other

3.3.3.2. Must Simplify to x

4. Continuity Test

4.1. Continuious

4.1.1. At a point

4.2. Discontinuious

4.2.1. Types of Dicontinuity

4.2.1.1. Removable

4.2.1.2. Jump

4.2.1.3. Infinite

6. Tables

6.3. Continuity test

6.3.1. Continuous

6.3.2. Discontinuous

7. Sets

7.2. Set Builder Notation

7.2.1. Number Sets

7.2.1.1. N

7.2.1.1.1. Naturals

7.2.1.2. W

7.2.1.2.1. Wholes

7.2.1.3. Z

7.2.1.3.1. Integers

7.2.1.4. Q

7.2.1.4.1. Rationals

7.2.1.5. R

7.2.1.5.1. Reals

7.2.1.6. I

7.2.1.6.1. Irrationals

7.3.1. Bounded

7.3.2. Unbounded

7.4. Unions and Intersections

7.4.1. Venn Diagram