Functions

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Functions by Mind Map: Functions

1. Types

1.1. Odd

1.1.1. ƒ(-x) = -ƒ(x)

1.2. Even

1.2.1. ƒ(-x) = ƒ(x)

2. Notations

2.1. Interval

2.2. Set Builder

2.2.1. Subsets

2.3. Limit

2.3.1. Continuity

2.3.1.1. Continuity Test

2.3.1.1.1. Continuous

2.3.1.1.2. Discontinuous

2.3.2. End Behavior

2.3.2.1. +/- infinity

2.3.2.2. Specific values

2.4. Function

2.4.1. Piecewise-Defined

3. Graphs

3.1. Rate of Change

3.1.1. (ƒ(x2)-ƒ(x1))÷(x2-x1)

3.2. Extrema

3.2.1. maximum

3.2.1.1. relative

3.2.1.2. absolute

3.2.2. minimum

3.2.2.1. relative

3.2.2.2. absolute

3.3. Increasing, Decreasing, & Constant

3.4. Domain & Range

3.5. Symmetry

3.5.1. Y-Axis

3.5.1.1. x,y = -x,y

3.5.2. X-Axis

3.5.2.1. x,y = x,-y

3.5.3. Origin

3.5.3.1. x,y = -x,-y

3.5.4. Asymmetric

3.6. Y-Intercepts

3.7. X-Intercepts

3.7.1. Zeros

3.7.1.1. Roots

4. Parent Funtions

4.1. Transformations

4.1.1. 1. Horizontal Shifts

4.1.1.1. Left

4.1.1.2. Right

4.1.2. 2. Dilations

4.1.2.1. Compress

4.1.2.1.1. Vertically

4.1.2.1.2. Horizontally

4.1.2.2. Stretch

4.1.2.2.1. Vertically

4.1.2.2.2. Horizontally

4.1.3. 3. Reflections

4.1.3.1. y-axis

4.1.3.2. x-axis

4.1.4. 4. Vertical Shifts

4.1.4.1. Up

4.1.4.2. Down

4.1.5. Absolute Value Transformations

4.1.5.1. |ƒ(x)|

4.1.5.2. ƒ(|x|)

4.2. Constant

4.2.1. ƒ(x)=c

4.3. Identity

4.3.1. ƒ(x)=x

4.4. Quadratic

4.4.1. ƒ(x)=x^2

4.5. Cubic

4.5.1. ƒ(x)=x^3

4.6. Square Root

4.6.1. ƒ(x)=√x

4.7. Reciprocal

4.7.1. ƒ(x)=1/x

4.8. Absolute Value

4.8.1. ƒ(x)=|x|

4.9. Greatest Integer

4.9.1. ƒ(x)=[[x]]

5. Inverse Functions

5.1. Horizontal Line Test

5.2. One-to-One

5.2.1. ƒ(x)=x^3

5.2.2. ƒ(x)=x

5.3. Restricted Domains

5.3.1. ƒ(x)=|x|

5.3.2. ƒ(x)=x^2

6. Composition Functions

6.1. (ƒ+g)(x)

6.2. (ƒ-g)(x)

6.3. (ĥg)(x)

6.4. (ƒ/g)(x)

6.5. (ļg)(x)