Functions
by Trace Markins
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. How to determine if a relation is a function
3.1. Algebraically
3.1.1. Input leads to one output
3.2. Graphically
3.2.1. Must pass Vertical Line Test
3.3. Numerically
3.3.1. Input leads to one output
4. Types
4.1. Piecewise define
4.2. Composite
4.2.1. Simplest form
4.2.1.1. Parent function
4.2.1.1.1. Transformations
4.3. Inverse
4.3.1. Horizontal Line test
4.3.2. One-to-One
5. Sets
5.1. Universal
5.2. Naturals
5.3. Wholes
5.4. Integers
5.5. Rationals
5.6. Reals
6. X and Y Axis
6.1. End behavior
6.2. Average Rate of Change
6.3. Range
6.4. Domain
6.5. Intercepts
6.6. Extrema
6.6.1. Absolute
6.6.2. Relative
7. Notations
7.1. Functions
7.2. Set-builder
7.3. Interval
7.3.1. Increasing
7.3.2. Constant
7.3.3. Decreasing
7.4. Limit
8. Can be described as
8.1. Even/Odd
8.2. Increasing, decreasing or constant
8.2.1. Extrema- point on a graph where a curve starts increasing or decreasing
8.2.1.1. Minimum
8.2.1.2. Maximum
8.3. Continuous
8.4. Discontinuous
8.4.1. Removable
8.4.2. Nonremovable
8.4.2.1. Infinite
8.4.2.2. Jump
9. Parent functions
9.1. Identity
9.2. Squared
9.3. Cubed
9.4. Square root
9.5. Reciprocal
9.6. Absolute
9.7. Constant
9.8. Greatest Integer
10. Transformations
10.1. Rigid
10.1.1. Absolute Value
10.1.2. Translations
10.1.3. Reflections
10.2. Nonrigid
10.2.1. Dialations
10.2.1.1. Compressed or Stretched
10.2.1.1.1. Vertically
10.2.1.1.2. Horizontally
11. Symmetry
11.1. origin
11.2. y-axis
11.3. x-axis
11.3.1. Zeros