Relation

RELATION
A
Relation
A relation is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to at least one member of the range.

FUNCTIONS
B
Functions are special relations.
Every set of ordered pairs is a relation, but every relation is not a function
Functions make up a subset of all relations.
A function is defined as a relation that is either one to one or many to one., i.e. no ordered pairs have the same first element.

TYPES OF FUNCTIONS
B

Surjective
Injective
Bijective
A function is bijective (one-to-one and onto or one-to-one correspondence) if every element of the codomain is mapped to by exactly one element of the domain. (That is, the function is both injective and surjective.)

NATURAL DOMAIN
C
Every relation has a domain, the set of (input) values over which it is defined. If the domain is not stated, by convention we take the domain to be the largest set of (real) numbers for which the expression defining the function can be evaluated.
We call this the "natural domain" of the function.
Domain
Range

TRANSLATIONS
D
Shift upward of downward
Shift to the right or left

TRANSLATIONS
D
Reflections