Functions

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Functions by Mind Map: 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

1.4. Domain and Range

1.5. Limits

1.5.1. End Behavior

1.5.1.1. Increasing, Decreasing, and Constant

1.5.2. Limit Notation

1.6. Average Rate of Change

1.7. Inverses

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

3.1.5. Quadratic 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

5. Piece-wise Functions

5.1. Determining

5.2. Graphing

5.3. Evaluating

5.4. Writing Piece-wise Functions

6. Tables

6.1. Zeros

6.2. Limits

6.3. Continuity test

6.3.1. Continuous

6.3.2. Discontinuous

6.4. End behavior

6.5. Odd and even

7. Sets

7.1. Set Notation

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. Interval Notation

7.3.1. Bounded

7.3.2. Unbounded

7.4. Unions and Intersections

7.4.1. Venn Diagram

8. Not a Function

8.1. Does Not Pass Vertical Line Test

8.2. X With More Than One Y

8.3. More Than One Output