Functions

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Functions by Mind Map: Functions

1. Piecewise Defined

1.1. notation

2. Characteristics

2.1. Intercepts

2.1.1. Y-Intercrepts

2.1.2. Zeros (X-intercepts)

2.2. Extrema

2.2.1. Relative

2.2.1.1. Min

2.2.1.2. Max

2.2.2. Absolute

2.2.2.1. Max

2.2.2.2. Min

2.3. Increasing, Decreasing, and Constant

2.4. Symmetry

2.4.1. origin

2.4.1.1. neither

2.4.2. x-axis

2.4.2.1. even

2.4.3. y-axis

2.4.3.1. odd

3. Sets

3.1. set notation

3.2. interval notation

3.3. set builder notation

3.4. Number groups

3.4.1. real

3.4.1.1. rational

3.4.1.1.1. integers

3.4.1.2. irrational

3.5. Universal Set

3.5.1. All numbers possible within a given example

4. graphs

4.1. Transformations

4.1.1. Translations

4.1.1.1. Vertical

4.1.1.2. Horizontal

4.1.2. Dilations

4.1.2.1. Vertical Compression

4.1.2.1.1. Change in y values

4.1.2.2. Vertical stretch

4.1.2.2.1. change in y values

4.1.2.3. Horizontal Compression

4.1.2.3.1. Change in x values

4.1.2.4. Horizontal Stretch

4.1.2.4.1. Change in x values

4.1.3. Reflection

4.1.3.1. over x-axis

4.1.3.2. over y axis

4.1.4. Absolute Value

4.1.4.1. f(x)=lxl+5

4.1.4.2. f(x)=lx+5l

4.2. Parent Functions

4.2.1. Identity

4.2.2. Cubic

4.2.3. Quadratic

4.2.4. Constant

4.2.5. Square root

4.2.6. Reciprocal function

4.2.7. Absolute Value

4.2.8. Greatest Integer

5. Equations

5.1. Average Rate of Change

5.1.1. Secant Line

5.2. Range

5.2.1. Interval Notation

5.2.2. Set-Builder Notation

5.3. Domain

5.3.1. Interval Notation

5.3.2. Set-Builder Notation

5.4. Operations on Functions

5.4.1. Addition

5.4.2. Subtraction

5.4.3. Multiplication

5.4.4. Division

5.5. Compositions of Functions

5.5.1. Real World Applications

5.5.2. Examples

5.5.2.1. (g o f)(x)

5.5.2.1.1. (g/f)(x)

5.5.2.2. (f o g)(x)

5.5.2.2.1. (f/g)(x)

5.5.3. Determining if functions have inverses.

5.6. Inverses

5.6.1. Flip x and y to find inverse.

5.6.2. (f o g)(x) and (g o f)(x) should both equal x

5.6.3. Domain and Range flips

5.6.4. coordinates reflect over the line f(x)=x

5.6.5. Notated f^-1(x)=x

5.7. Factoring

5.7.1. GCF

5.7.1.1. 4 terms

5.7.1.2. Perfect Squares

5.7.1.3. Coefficient of 1

5.7.1.4. Coefficient of Greater than 1

5.8. Zeros and y-intercepts

6. Limits

6.1. Limit Notation

6.1.1. End Behavior

7. Continuity

7.1. Continuity Test

7.1.1. Continuous

7.1.1.1. lim f(x) as x approaches limit= f(x)

7.1.2. Discontinuous

7.1.2.1. removable

7.1.2.2. non removable

7.1.2.2.1. infinite

7.1.2.2.2. jump