Linear Programming

Vertices:	-6,0		0,4		0,0
Constraints	Objective Function:
x ≥ 0 y ≤8 -2x + 3y≥  12	C=4x+6y  C=4(-6)+6(0) C=-24	C=4(0)+6(4) C=24		C=4(0)+6(0) C=0

Vertices:	1,8		1,2		5,2
Constraints	Objective Function:
x ≥ 1 y ≥ 2 6x +4 y ≤ 38	C=7x+3y  C=7(1)+3(8) C=31	C=7(1)+3(2) C=13		C=7(5)+3(2) C=41

Vertices:	-5,4		5,8		5,4
Constraints	Objective Function:
x≤ 5 y ≥ 4 -2x +3 y ≤ 30	C=2x+5y  C=2(-5)+5(4)  C=10	C=2(5)+5(8) C=50		C=2(5)+5(4) C=30

Vertices:	0,6		0,0		6,0
Constraints	Objective Function:
x ≥ 0 y ≥ 0 x + y ≤ 6	C=3x+4y C=3(0)+4(6)	24		C=3(0)+4(0)		0		C=3(6)+4(0) 18

Vertices:
Constraints	Objective Function:
x ≥ 0 y ≥ 0 4x + 4y ≤ 20 x+2y≤8

Statistics Test

Statistic TestStatistic Test

Graphing Exponetial Growth & Decay

Y= a×b x-h +K

A= multiplier

A>1= stretch

A<a<1= compression

A<0 (negative) = flipped over x- axis.

B= base has an exponential (always positive)

0>b<1= Decay (always decreasing)

Asymptote

y=k

Domain

(-∞, ∞) =all real numbers

Range

y>k (a is pos)

y<k (a is neg)

Exponential equations domain is always all real numbers.