Transformations

                                                      
                             
                                 http://www.mathplayground.com/ShapeMods/ShapeMods.html

Compound Interest

Formula:

P = principal amount (the initial amount you borrow or deposit) r  = annual rate of interest (as a decimal) t  = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. n  =  number of times the interest is compounded per year

Example

An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. What is the balance after 6 years?

                                                                           Solution

Using the compound interest formula, we have that P = 1500, r = 4.3/100 = 0.043, n = 4, t = 6. Therefore, So, the balance after 6 years is approximately $1,938.84.

Liner Programming

<<<Image Goes Here>>>
Vertices: (0,6) (0,0) (6,0)
Constraints	Objective Function:
x ≥ 0 y ≥ 0 x + y ≤ 6				C + 3x = 4y

<<<Image Goes Here>>>
Vertices: (0,6) (-5,4) (0,4)
Constraints	Objective Function:
x ≤ 5 y ≥ 4 -2x + 5y ≤ 30				C = 2x + 5y

<<<Image Goes Here>>>
Vertices: (1,8) (1,2) (5,2)
Constraints	Objective Function:
x ≥ 0 y ≥ 0 x + y ≤ 5		C + 7x + 3y

<<<Image Goes Here>>>
Vertices: (0,8) (0,4) (6,8)
Constraints	Objective Function:
x ≥ 0 y ≥ 8 -2x +3 y ≤ 12		C = 4x + 6y

<<<Image Goes Here>>>
Vertices: (0,5) (0,4) (2,3)
Constraints	Objective Function:
x ≥ 0 y ≥ 0 4x +4 y ≤ 20 x + 2y ≤ 8		C = 8x + 7y

<<<Image Goes Here>>>
Vertices: (0,4) (0,2) (3,0) (4,3)
Constraints	Objective Function:
x ≥ 0 2x + 3y ≥ 6 3x - y ≤ 9 x +4 y ≤ 16		C = 3x + 5y

Graphing Exponential Growth/Decay

Graphing Exponential Growth/Decay

•  Formula: y=a*bx-h+k

• a= multiplier (greater than, vertical stretch, if a is in between o & l it"s a vertical compression, if it gets flipped)
• b= base (either a number between o &1 or greater than 1)
• h= left/right  (up)
• k= up/down
• domain= (
• asmtope= (y=k) r+ range y<k when a s negative & y > k when a is positive

 Negative exponents mean to FLIP A FRACTION

Characteristics and Traits of Graphs

Domain - Determine how far left & right the graph goes

Range - Determines how far up & down the graph goes

End Behavior - Describes the 2 ends of an equation

Absolute Max/Min - point that highest/lowest on the graph

Local Max/Min -More than one point that is the highest or lowest 

Interval of increase - point where it increases the x axis

Interval of decrease - section of graphs when y values are decreasing

X intercept - point where it crosses the x axis

Y intercept - point where it crosses the y axis

Symmetry - even: symmetric at y axis
                  odd: symmetric at orgion 
             neither: no symmetry

Asymptotes - imaginary line closer & closer to the line but never touches it

Function - passes vertical line test

This is an example of a line failing the vertical line test so...

NOT A FUNCTION!

 One to One - passes vertical & horizontal line test