Thursday, March 20, 2014

Graphing Exponential Growth/Decay

Graphing Exponential Growth/Decay

1. Create the Parent Graph.
2. Identify A,H,K.
3. Create your new T-Chart.

Domain: All real #'s.
Range: y>k; when a is positive. y<k; when a is negative.
Asymptote: y=k.
4. Draw Asymptote.
5. Graph new points.
Exponential Formula:  y=a×bx-h+k
a = multiplier.
a>1 = stretch
0<a<1 = compression
a< 0(negative) = flipped over x-axis.
b = base
b>1 = whole #, growth, always increasing.
0<b<1 = fraction; decay, always decreasing.
B is never negative only the multiplier is.
h = lf/rt; opposite
k = up/dn

Linear Programming

                               
Vertices:
 (0,0) 
 (0,6) 
 (6,0) 

Constraints
Objective Function: C=4x + 6y 
x > 0
y > 0
x + y < 6







                                

Vertices:
 (-5,4) 
 (0,6)
 (5,0) 

Constraints
Objective Function: C= 8x + 7y
x < 5
y > 4
-2x + 5y < 30














Vertices:
 (0,2) 
 (1,0) 
 (5,2) 

Constraints
Objective Function: C= 7x + 3y 
x > 1
y > 2
6x + 4y < 38








<<<Image Goes Here>>>
Vertices:
 (0,4)
 (-6,0)
 (0,0)

Constraints
Objective Function: C= 4r + 6y
x>0
y<8
-2r+3y>12





      



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





                               



Vertices:
 (0,2)
 (3,0)
 (0,-9)

Constraints
Objective Function: C=3x+5y
x>0
2x+3y>6
3x-y<9
x+4y<16






Thursday, February 27, 2014

Tuesday, January 28, 2014

Arithmetic And Geometric Sequence

Arithmetic & Geometric Sequences 
A sequence is a list of numbers. 

General Form of an Arithmetic Sequence


an a1 +(n - 1)d



General Form of an Geometric Sequence

an = a1·rn-1
An arithmetic sequence represents a linear function. 

 
Arithmetic Sequence 
This video introduces arithmetic sequences. 
www.youtube.com/watch?v=jExpsJTu9o8

Geometric Sequence
This video introduces geometric sequences.

Tuesday, January 14, 2014

Characteristics and Traits

Domain- X Values - How far left or right the graph goes. 
Range- Y Values- How far up or down the graph goes.
End Behavior- Describing the two ends of the equation
Absolute Max/Min- 1 point that is highest or lowest on a graph. (x,y)
Local Max/Min- More than 1 point that is highest or lowest on the graph.
Interval of Increase- Intercept point of rising x and y values
Interval of Decrease- Intercept points of falling x and y values.
Symmetry- Even is symmetric across the x axis, odd is symmetric across the origin, neither has no symmetry.
X intercept- Intercept point of the x-value
Y intercept-  Intercept point of the y-value
Function- Passes the vertical line test.
One to One- Passes both vertical and horizontal line test.
Domain & Range 
End Behavior 

Absolute Max/Min 
Local Max/Min
X & Y Intercept 
Symmetry 

Function- Vertical Line Test 
One to One- Horizontal Line Test