Functions

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Functions by Mind Map: Functions

1. Combinations and Compositions

1.1. Arithmetic Combinations

1.1.1. f(g(x))

1.1.2. (f - g)(x)

1.1.3. (f + g)(x)

1.1.4. (f/g)(x)

1.1.5. g(f(x))

1.1.6. (f * g)(x)

2. Tranformations

2.1. Translation

2.2. Dilation

2.3. Reflection

3. Piecewise

3.1. real life sitations

3.2. graphing

4. Sets

4.1. Subsets

4.1.1. Interval Notation

4.1.1.1. ( most negative #, most postive # )

4.1.1.2. Bounded

4.1.1.2.1. [3,1)

4.1.1.3. Unbounded

4.1.1.3.1. (3,infinty)

4.1.2. Limit Notation

4.1.2.1. End Behavior

4.1.2.2. Continuity

4.1.2.2.1. Continuous

4.1.2.2.2. Discountinuous

4.1.3. Set Builder Notation

4.1.3.1. {variable | describe properties of #s , ID the # set}

4.1.4. Set Notation

4.1.4.1. ( most negative #, most postive # )

4.2. Universal Set

4.2.1. unions

4.2.2. intersections

4.2.3. empty

5. Characterizing Functions

5.1. Intervals of Functions

5.1.1. Constant

5.1.2. Increasing

5.1.3. Decreasing

5.1.4. Odd /Even/ Neither

5.1.4.1. Algebraic test

5.1.4.1.1. Even F(-x)= F(x)

5.1.4.1.2. Odd F(-x)=-F(x)

5.1.4.2. Type of function

5.1.5. Extrema

5.1.5.1. Relative

5.1.5.2. Absolute

5.2. Symmertry

5.2.1. x -axis

5.2.2. y - axis

5.2.3. orgin

5.3. Range

5.3.1. All possible y values in a function

5.4. Zeros

5.4.1. What is x when y=0?

5.4.1.1. Look in charts to see when y changes from (+) to (-)

5.5. y-intercept

5.5.1. What is y when x=0?

5.5.1.1. Plug 0 into x and solve

5.6. Parent Functions

5.6.1. Reciprocal

5.6.1.1. f(x)=1/x

5.6.2. Square Root

5.6.2.1. f(x)=√x

5.6.3. Cubic

5.6.3.1. f(x)=x^3

5.6.4. Quadratic

5.6.4.1. f(x)=x^2

5.6.5. Identity

5.6.5.1. f(x)=x

5.6.6. Constant

5.6.6.1. f(x)=c

5.6.7. Step

5.6.7.1. f(x)={[x]}

5.7. Limits

5.8. Domain

5.8.1. All possible x values in a function