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# Algebra II

formulas and definitions

AB
complex numbershave the form a+bi where a and b are real and i=square root of -1
Real numbershave points on the number line
imaginary numberssquare roots of a negitive number. no points on the number line
negitive numbersnumbers less than zero
zeroneither positive or negitive
positive numbersnumbers greater than zero
Rational numberscan be expressed exactly as the ratio of two numbers
irrational numberscannot be expressed excatly as a ratioof two integers, but are real numbers
integerwhole numbers and there opposites
nonintergersfractions
raticlesroots of integers
transcendental numberscannot be expressed as roots or integers
natural numberspositive integers or counting numbers
digitsnumbers from which the numerals are made
even numbersintegers divisible by two
odd numbersintegers not divisible by 2
closureclosed under addition and under multiplication
commutativityaddition and multiplication of real numbers you can flip them around
Associativitymoving parentesis
identityx+0=x or x*1=x
inversesx+(-x)=0 or x*1/x=1
polynomialmany terms
degree of a polynomialmaximum # of variables that appear as factors in any one form
solving an equationsolving its solution set
extraneoussatisfies a transformed equation not the original
reflexive propertyx=x
domainset of values for independant variable
rangeset of values for depandant varible
asympoteline that gets close to but never touches
relationnon function 2 values for x for one value for y
function1 value for x for one value for y
linear functiony=mx+b
y-interseptx=0
x-intersepty=0
m=sloperise/run
slope formulay2-y/x2-x=slope
horizontal liney=# slope equal 0
vertical linex=# slope=none
point-slope formy-y1=m(x-x1)
standard formAx+By=C
parallelsame slope
perpinicularslope -1/m
systemequations or inequalities is a set of open sentences which contain the same varible
solution set2 varibles is a set of ordered pairsthat satisfied all of the open sentences
f(x)y