Functions

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Functions by Mind Map: Functions

1. Subsets

1.1. Bounded

1.2. Unbounded

1.3. Elements

1.4. Real Numbers

1.5. Intersections

1.6. Unions

2. Definition

2.1. Is a relation that assigns each element in the domain exactly one element in the range

3. Notations

3.1. Functions

3.2. Set-builder

3.3. Interval

3.3.1. Increasing

3.3.2. Constant

3.3.3. Decreasing

3.4. Limit

4. Can be described as

4.1. Even/Odd

4.2. Increasing, decreasing or constant

4.2.1. Extrema- point on a graph where a curve starts increasing or decreasing

4.2.1.1. Minimum

4.2.1.2. Maximum

4.3. Continuous

4.4. Discontinuous

4.4.1. Removable

4.4.2. Nonremovable

4.4.2.1. Infinite

4.4.2.2. Jump

5. Parent functions

5.1. Identity

5.2. Squared

5.3. Cubed

5.4. Square root

5.5. Reciprocal

5.6. Absolute

5.7. Constant

5.8. Greatest Integer

6. Transformations

6.1. Rigid

6.1.1. Absolute Value

6.1.2. Translations

6.1.3. Reflections

6.2. Nonrigid

6.2.1. Dialations

6.2.1.1. Compressed or Stretched

6.2.1.1.1. Vertically

6.2.1.1.2. Horizontally

7. How to determine if a relation is a function

7.1. Algebraically

7.1.1. Input leads to one output

7.2. Graphically

7.2.1. Must pass Vertical Line Test

7.3. Numerically

7.3.1. Input leads to one output

8. Types

8.1. Piecewise define

8.2. Composite

8.2.1. Simplest form

8.2.1.1. Parent function

8.2.1.1.1. Transformations

8.3. Inverse

8.3.1. Horizontal Line test

8.3.2. One-to-One

9. Sets

9.1. Universal

9.2. Naturals

9.3. Wholes

9.4. Integers

9.5. Rationals

9.6. Reals

10. Symmetry

10.1. origin

10.2. y-axis

10.3. x-axis

10.3.1. Zeros

11. Domain

12. Range

13. Inverse

13.1. Positive

13.2. Negative

13.3. Even

13.4. Odd

14. X and Y Axis

14.1. End behavior

14.2. Average Rate of Change

14.3. Range

14.4. Domain

14.5. Intercepts

14.6. Extrema

14.6.1. Absolute

14.6.2. Relative