Functions

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Functions by Mind Map: Functions

1. Discontinuos

1.1. Removable

1.1.1. As x --> c the y values approach the same value from both sides.

1.2. Infinite

1.2.1. As x--> c the y values increase or decrease without bound

1.3. jump

1.3.1. As x--> c the y values approach different values from both sides

2. graphs

2.1. domain

2.1.1. set builder

2.1.1.1. Number sets: R,Q,Z,I .. ect.

2.1.2. interval notation

2.1.2.1. (X1,X2), ex: (3,17)

2.2. range

2.3. piecewise defined functions

2.3.1. .

2.3.2. .

2.4. symmetry

2.4.1. origin

2.4.1.1. f(x)=-f(x)

2.4.1.1.1. odd

2.4.1.2. .

2.4.2. y axis

2.4.2.1. f(x)=f(-x)

2.4.2.1.1. even

2.4.2.2. .

2.4.3. x axis

2.4.3.1. f(-x)=-f(x)

2.4.3.1.1. neither

2.4.3.2. .

2.5. transformations

2.5.1. vertical translations

2.5.1.1. k units up when K>0

2.5.1.2. K units down when K<0

2.5.2. horizontal translations

2.5.2.1. h units right when h>0

2.5.2.2. h units left when h<0

2.5.3. reflection in the x-axis

2.5.3.1. y=f(x)

2.5.3.1.1. y=-f(x)

2.5.3.2. .

2.5.4. reflection in the y-axis

2.5.4.1. y=f(x)

2.5.4.1.1. y=f(-x)

2.5.4.2. .

2.6. zeros

2.6.1. Same thing as x intercepts. Have the equation equal to zero.

2.7. y-intercepts

2.7.1. For x put zero in.

2.8. vertical line test

2.8.1. inverse functions

2.9. one-to-one

2.9.1. horizontal line test

2.9.1.1. inverse functions

2.10. end behavior

2.10.1. limit notation

2.10.1.1. .

2.11. tables

2.11.1. x and y

2.11.1.1. one x to one y

2.12. Increasing

2.12.1. decreasing

2.12.1.1. constant

2.12.1.1.1. rate of change

2.13. extrema

2.13.1. max

2.13.2. min

2.13.3. increasing

2.13.3.1. x values representing the increase of a graph

2.13.4. decreasing

2.13.4.1. x values representing the decrease of a graph

2.13.5. constant

2.13.5.1. a point on the graph, where the it is neither increasing nor decreasing.

2.13.6. absolute min

2.13.6.1. the lowest point of the graph

2.13.7. absolute max

2.13.7.1. the highest point of the graph

2.13.8. relative min

2.13.8.1. A minimum point on the graph, but is between the highest and lowest values. May be more than one.

2.13.9. relative max

2.13.9.1. A maximum point on the graph, is in between the highest and lowest values. May be more than one.

3. parent functions

3.1. quadratic ,

3.1.1. X^2

3.1.2. .

3.2. greatest integer,

3.2.1. [[X]]

3.2.2. .

3.3. reciprocal

3.3.1. 1/X

3.3.2. .

3.4. Square root

3.4.1. .

3.4.2. .

3.5. Absolute Value

3.5.1. |X|

3.5.2. .

3.6. constant

3.6.1. f(x)=c

3.6.2. f(x)=c

3.7. cubic

3.7.1. X^3

3.7.2. .

3.8. identity

3.8.1. Y=X

3.8.2. .

4. equations

4.1. factoring

4.1.1. diff. of cubes

4.1.1.1. sum of cubes

4.1.2. grouping

4.1.3. trinomials

4.1.4. diff. of squares

4.1.5. greatest common factor

4.2. inverse

4.2.1. verifying

4.2.2. graphs

4.2.2.1. own inverses

4.2.2.2. reflects over the graph of the line Y=X

4.3. algebra

4.3.1. zeros

4.3.2. y intercepts