Functions

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Functions by Mind Map: Functions

1. Functions

2. Sets

2.1. Reals

2.1.1. Rational

2.1.1.1. Integers

2.1.1.2. Wholes

2.1.1.3. Naturals

2.1.2. Irrational

2.2. Universal set

2.2.1. Unions

2.2.1.1. U

2.2.1.2. "or"

2.2.2. Intersections

2.2.2.1. "and"

2.2.2.2. ∩

2.2.3. Empty Set

3. Notation

3.1. Interval

3.1.1. Unbounded

3.1.2. bounded

3.1.3. inequalities

3.2. Function Notation

3.2.1. Independent Variable

3.2.2. Dependent Variable

3.3. Set-builder

3.3.1. properties

4. Behavior

4.1. End Behavior

4.1.1. Right End

4.1.1.1. lim f(x)

4.1.2. Left End

4.1.2.1. lim f(x)

4.2. Extrema

4.2.1. Minimum

4.2.2. Maximum

5. Graphing

5.1. Symmetry

5.1.1. Origin

5.1.1.1. ODD

5.1.2. Point Symmetry

5.1.3. Line Symmetry

5.1.4. Y-axis

5.1.4.1. EVEN

5.1.5. X-axis

5.2. Range

5.2.1. Y-intercept

5.3. Domain

5.3.1. Implied

5.3.2. Relevent

5.3.3. X-intercept

5.3.3.1. Zeros

5.3.3.1.1. Roots

5.4. Average Rate of Change

5.4.1. Secant line

5.4.2. Average Rate of Change Formula

6. Continuity Test

6.1. Continuous

6.1.1. Limit

6.2. Discontinuous

6.2.1. Removable

6.2.2. Nonremovable

6.2.2.1. Jump

6.2.2.2. Infinite

7. Parent Functions

7.1. f(x)=/x/

7.1.1. Absolute Value

7.2. f(x)=C

7.2.1. Constant Function

7.2.2. Zero Function

7.3. f(x)=x

7.3.1. Identity Function

7.4. f(x)=x^2

7.4.1. Quadratic Function

7.5. f(x)=x^3

7.5.1. (picture Here)

7.5.2. Cubic Function

7.6. f(x) = 1/x

7.6.1. Reciprocal Function

7.7. f(x) = √x

7.7.1. (picture here)

7.7.2. Square Root Function

7.8. Inverse

7.8.1. f(g(x))

7.8.1.1. (fog)(x)

7.8.2. Every domain has one corresponding range and every range has one corresponding domain.

7.8.2.1. one to one

7.8.3. f^-1(x)

7.8.4. Is It's own inverse

7.8.5. Inverse is not a function as it stands.

7.9. Transformations

7.9.1. Dilations

7.9.1.1. Horizontal Compression

7.9.1.1.1. g(x)= f(ax); a>1

7.9.1.2. Horizontal Stretch

7.9.1.2.1. g(x)= f(ax); 0<a<1

7.9.1.3. Vertical Stretch

7.9.1.3.1. g(x)= af(x); a>1

7.9.1.4. Vertical Compression

7.9.1.4.1. g(x)= af(x); 0<a<1

7.9.2. Reflections

7.9.2.1. Over Y-axis

7.9.2.1.1. g(x)= -f(x)

7.9.2.2. Over X-axis

7.9.2.2.1. g(x)- f(-x)

7.9.3. Translations

7.9.3.1. Vertical

7.9.3.1.1. Up

7.9.3.1.2. Down

7.9.3.2. Horizontal

7.9.3.2.1. Left

7.9.3.2.2. Right

8. BY: CYERENA SHARP, LEXUS BROSH, CARI COY

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