FUNCTIONS
by Jessica Saini
1. Extrema
1.1. Relative Minimum
1.2. Relative Maximum
1.3. Absolute Minimum
1.4. Absolute Maximum
2. Domain
2.1. Relevant Domain
2.2. Implied Domain
3. Piece-wise Defined Functions
4. Greatest Integer Function
5. Absolute Value Function
6. Intervals
6.1. Increasing
6.2. Decreasing
6.3. Constant
7. Transformtions
7.1. Rigid
7.1.1. Dialations
7.1.1.1. Vertical Stretch
7.1.1.2. Vertical Compression
7.1.1.3. Horizontal Compression
7.1.1.4. Horizontal Stretch
7.2. Non-Rigid
7.2.1. Tranlations
7.2.1.1. Vertical
7.2.1.2. Horizontal
7.2.2. Reflections
7.2.2.1. Reflection Over y-axis
7.2.2.2. Reflection Over x-axis
8. Vertical Line Test
9. Range
10. Sets
10.1. Set Notation
10.1.1. Subsets
10.1.1.1. Elements
10.2. Set Builder Notation
10.2.1. Subsets
10.2.1.1. Elements
10.3. Interval Notation
10.3.1. Subsets
10.3.1.1. Elements
10.4. Venn Diagrams
10.5. Unions
10.6. Intersections
11. Real Numbers
11.1. Irrational Numbers
11.2. Natural Numbers
11.3. Whole Numbers
11.3.1. Natural Numbers
11.4. Integers
11.4.1. Natural Numbers
11.4.2. Whole Numbers
11.5. Rational Numbers
11.5.1. Natural Numbers
11.5.2. Whole Numbers
11.5.3. Integers
12. Symmetry
12.1. x-axis
12.2. y-axis
12.2.1. Even Functions
12.3. origin/point
12.3.1. Odd Functions
13. Parent Functions
13.1. Constant Function: f(x) = c
13.2. Identity/Linear Function: f(x) = x
13.3. Quadratic Function: f(x) = x^2
13.4. Cubic Function: f(x) = x^3
13.5. Radical/Square Root Function: f(x) = square root of x
13.6. Reciprocal Function: f(x) = 1 / x
14. Limits
14.1. Limit Notation
14.1.1. End Behavior
14.2. Continuity Test
14.2.1. Continuities
14.2.2. Discontinuities
14.2.2.1. Removable
14.2.2.2. Non-Removable
14.2.2.2.1. Jump
14.2.2.2.2. Infinite
15. Arithmetic Combinations
16. Compositions
17. Inverses
17.1. Horizontal Line Test
17.1.1. One-to-One Functions