Functions

1. Graphing Functions

1.1. Domain

1.1.1. Set Notation

1.1.2. Interval Notation

1.1.3. Set Builder Notation

1.2. Symmetry

1.2.1. x-axis

1.2.1.1. Fails vertical line test

1.2.2. y-axis (even)

1.2.3. origin (odd)

1.3. Extrema

1.3.1. Absolute Maximum

1.3.1.1. Decreasing

1.3.2. Relative Max/Min

1.3.3. Absolute Minimum

1.3.3.1. Increasing

1.4. Finding Zeros (factor) and y intercepts

2. Real World Problems

2.1. Piecewise Functions

2.2. Average Rate of Change

3. Behavior of Functions

3.1. End Behavior

3.2. Continuity Test

3.2.1. Continuous

3.2.1.1. Limit

3.2.2. Discontinuous

3.2.2.1. Infinite, Jump, Removable

4. Parent Functions

4.1. Transformations

4.1.1. Horizontal, Dilations, Reflections, Vertical

4.2. Compositions

4.2.1. [f º g] or [g º f]

4.3. Inverse Functions

4.3.1. One-to-One (horizontal line test)

4.4. Absolute Value Transformations

4.4.1. f(|x|) Input = non negative

4.4.2. |f(x)| Output = non negative