Unit 1 & 2 OnRamps Algebra II

Natural Numbers

1,2,3,4,5,............ (N)

Integers

-3,-2,-1,0,1,2,3,...... (Z)

Rational Numbers

Numbers of the form a/b where a and b are integers and b ≠ 0. Basically anything that can be written as a fraction. (Q)

Irrational Numbers

Everything that isn't rational (Q to the power of c)

Real Numbers

All rational and irrational numbers. All numbers that have points on a number line.(R)

Complex Numbers

In the form of x+yi where x and y are elements of real numbers and i=square root of -1. (C)

is an element of or belongs to

∈

there exists

∃

for all or for every

∀

such that

: or |

an implication or mapping (when used with functions).

→

Closure Addition

x+y (y is a real number)

Closure Multiplication

x(y) (y is a real number)

Commutative Addition

x+ y=y +x

Commutative Multiplication

x(y)=y(x)

Associative Addtion

(x+y) +z= x+(y+z)

Associative Multiplication

(xy)z=x(yz)

Identity Addition

x+0=x

Identity Multiplication

x(1)=x

Inverse Addition

x+(-x)=0

Inverse Multiplication

x(1/x)=1 for x≠0

Distribution Rule

x(y+z)=xy+xz

x intercept

what is x when y=0

y intercept

what is y when x=0

linear function

f(x)=x

quadratic function

f(x)=x²

absolute value function

f(x)=|x|

horizontal shift

positive will go left

negative will go right

vertical shift

positive will shift up

negative will go down

reflection across the x axis

-f(x) (i.e. -(x+5))

reflection across the y axis

f(-x) (i.e. (-x-10))