1. Algebraically
1.1. Domain and Range
1.1.1. Interval Notation
1.2. Y-intercept and Zeros
1.3. Continuity
1.3.1. Continuity Test
1.3.2. Discontinuity
1.3.2.1. Removable
1.3.2.2. Infinite
1.3.2.3. Jump
1.4. End Behavior
1.4.1. Limit Notation
1.5. Limits
1.5.1. Limit Notation
1.6. Transformations
1.7. Piecewise-Defined
1.8. Average Rate of Change
1.8.1. Rise over run
1.9. Combinations of Functions
1.10. Compositions of Functions
1.11. Inverses
1.11.1. Horizontal Line Test
1.11.2. f(g(x)) = x and g(f(x)) = x
2. Graphically
2.1. Domain and Range
2.1.1. Interval Notation
2.2. Y-intercept and Zeros
2.3. Continuity
2.3.1. Continuity Test
2.3.2. Discontinuity
2.3.2.1. Removable
2.3.2.2. Infinite
2.3.2.3. Jump
2.4. End Behavior
2.4.1. Limit Notation
2.5. Extremas
2.5.1. Absolute and Relative
2.6. Transformations
2.7. Piecewise-Defined
2.8. Average Rate of Change
2.8.1. Rise over run
2.9. Combinations of Functions
2.10. Compositions of Functions
2.11. Inverses
2.11.1. Horizontal Line Test
2.11.2. f(g(x)) = x and g(f(x)) = x
2.12. Symmetry
2.12.1. Equation
2.12.2. Function
2.13. Intervals
2.13.1. Increasing
2.13.2. Decreasing
2.13.3. Constant
2.14. Parent Functions
2.14.1. Identity Function: f(x) = c
2.14.2. Constant Function: f(x) = x
2.14.3. Square Function: f(x) = x^2
2.14.4. Cube Function: f(x) = x^3
2.14.5. Square Root Function: f(x) = √x
2.14.6. Reciprocal Function: f(x) = 1/x
3. Numerically
3.1. Domain and Range
3.1.1. Interval Notation
3.2. Y-intercept and Zeros
3.3. Continuity
3.3.1. Continuity Test
3.3.2. Discontinuity
3.3.2.1. Removable
3.3.2.2. Infinite
3.3.2.3. Jump
3.4. End Behavior
3.4.1. Limit Notation
3.5. Limits
3.5.1. Limit Notation
3.6. Symmetry
3.6.1. Equation
3.6.2. Function