Functions

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Functions by Mind Map: Functions

1. notations

1.1. set: {#}

1.2. set builder: {x | -3 < x ≤ 2}

1.3. interval: (-∞, -5] U (3, ∞)

2. Sets & Subsets

2.1. Elements {E} part of set

2.2. Empty Set

2.3. Universal

2.3.1. Subset

2.3.2. Unions & Intersections

3. Types

3.1. Parent Functions

3.1.1. Absolute Value Function

3.1.1.1. |f(x)|

3.1.1.2. f(|x|)

3.1.2. Constant/Zero Function f(x)=C

3.1.3. Identity Function f(x)=x

3.1.4. Quadratic Function f(x)=x^2

3.1.5. Square Root Function f(x)= √x

3.1.6. Cubic Function f(x)=x^3

3.1.7. Reciprocal Function f(x)=1/x

3.1.8. Greatest Integer Function f(x)= [[x]]

3.2. Special Functions

3.2.1. piece-wise functions (include boundaries)

3.2.1.1. domain

3.2.1.1.1. x/# set domain =0 ,restrict, use interval notation

3.2.1.1.2. √x+# set greater than or equal to 0

3.2.1.1.3. left to right on graph

3.2.1.2. range

3.2.1.2.1. up and down on graph

4. Limits

4.1. End behavior

4.1.1. approaching specific values

4.1.2. Extrema

4.1.2.1. Finding Average rate of change

4.1.2.1.1. m sec= f(x)2-f(x)1/ x2-x1

4.1.2.1.2. estimating absolute and relative extrema

4.1.2.2. Analyzing increasing and decreasing behavior/constants

4.1.3. lim f(x)= L as x approaches a certain value

4.2. limf(x)=L

5. Transformations

5.1. Reflections

5.2. Translations

5.2.1. Vertical

5.2.2. Horizontal

5.3. Dialations

5.3.1. Compress

5.3.2. Strech

6. Graphing

6.1. Continuity

6.1.1. Testing

6.1.1.1. Continuous

6.1.1.1.1. Table: f(x)lim=f(x) as x approaches c

6.1.1.2. Discontinuous

6.1.1.2.1. Removable

6.1.1.2.2. Infinite

6.1.1.2.3. Jump

6.2. Symmetry

6.2.1. X-axis

6.2.2. Y-axis

6.2.3. Origin

6.2.3.1. Even, Odd, or Neither

6.3. zeroes (crosses x-axis)

6.4. y-intercept (crosses y-axis)

7. Combinations and compositions

7.1. Inverses

7.1.1. Horizontal Line Test

7.2. (f+g) (f*g) (F o g) (F-g) (f/g) (g o f)