Functions
by Kara Combs
1. Absolute Maximum
1.1. Absolute Minimum
2. Relative Minimum
2.1. Odd graph test = -f(x) = f(-x)
3. Transformations
3.1. Slides/Translations
3.2. Dilatons-horizontal or vertical
3.3. Reflections
3.3.1. 1) reflect over the y-axis ex: g(x)=(-x)
3.3.2. 2) reflect over the x-axis ex: g(x)=-(x)
3.4. Graphing
3.4.1. 1.) horizontal shifts 2.) dilations 3.) reflections 4.) vertical shifts
4. Continuity Test
4.1. continuous if f(c) exists, f(x) approaches the same value from either side, the value f(x) approaches from each side of c is f(c)
4.2. if it does not meet these conditions then it is discontinuous
4.3. Jump, Removable, Infinite Discontinuities
5. Extrema
5.1. Relative Maximum
5.2. A value that is extreme compared to the
5.3. Graphs
5.3.1. Even graph test = f(x) = f(-x)
6. End Behavior
6.1. Where the graph seems to go.
6.2. limit notation
7. Parent Functions
7.1. Constant/Zero (2= x)
7.2. Identity (Y=X)
7.3. Quadratic (Y=x^2)
7.4. Cubic (Y=x^3)
7.5. Reciprocal (Y=1/X)
7.6. Absolute Value (| x |)
7.7. Greatest Integer (( [X] ))
7.8. Square Root (√x)
8. How to know if a relation is a function
8.1. Vertical line test
8.2. For every x there is one Y
9. Sets and Subsets
9.1. Unions are all the numbers in both sets
9.2. Intersections are numbers that appear in both sets, can not only appear in one
9.3. Universal Sets
9.3.1. Sets of all possible element
10. Notations
10.1. Set Builder Notation
10.1.1. {S | x>8, x=Q}
10.2. Interval notation
10.2.1. Use brackets (,),[, and ] to describe the range or domain
10.3. Piece-wise functions
11. Y and X intercepts
11.1. To find the Y intercept replaced the X intercepts with zeros and solve for Y.
11.2. To find the X intercept, replace the Y values with zero. Solve for x to find any zeros.
12. Equations
12.1. factoring
12.1.1. GCF
12.1.2. difference of squares
12.1.3. difference & sum of cubes
12.2. find zeros & y-intercept
13. Combinations and Compositions
13.1. Arithmetic
13.2. Domain and Range flip from original function
13.3. Inverse Functions
13.3.1. Testing for inverse functions-use horizontal line test