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