with

is the order of the polynomial
are called coefficients

is a root of if

a polynomial of order has roots (counting multiplicities) in

y=kx+b

is the slope and determines the direction

is the intercept (on the -axis)

is also the tangent of the angle between the line and the x-axis

if the line crosses and with , then

determines to which side the graph is opening

it may have 0,1 or 2 real roots

roots at

attains a maximum/minimum at

if , then
is written as

defined on entire

omits all non-positive values (in particular, NEVER 0)

monotonically increasing, and increases drastically fast (faster than any polynomials)

defined only for positive

assumes all values in (in particular, has one root at )

monotonically increasing, but increases pathetically slow (slower than any polynomials)

a sequence is a function with domain in

usually we take subsripts in or and write the sequence out by enumeration:

it can be defined explicitly, e.g.,
or recursively, e.g.,

a sequence of form (i.e., ) is called an arithemetic progression

is the common difference

a sequence of form (i.e., ) is called a geometric sequence

is the common ratio