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FUNCTIONS 
Definition of Function
"A function is a correspondence, or rule, that pairs each element of a set (The Domain) with exactly one element of another set. (The Range)"
What is the "Domain" ?
"The domain of a function is the set of its possible inputs, the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs."
What is the "Range" ?
"The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in."
What is the "Image" ?
In mathematics, the image of a function is the set of all output values it may produce.
Types of Functions
Unit Function
"In number theory, the unit function is a completely multiplicative function on the positive integers defined as: It is called the unit function because it is the identity element for Dirichlet convolution."
Constant Function
"In mathematics, a constant function is a function whose (output) value is the same for every input value."
Linear Function
"A mathematical function in which the variables appear only in the first degree, are multiplied by constants, and are combined only by addition and subtraction."
One to One Function
"A one-to-one function is a function of which the answers never repeat. For example, the function f(x) = x + 1 is a one-to-one function because it produces a different answer for every input."
Piecewise Defined Function
"We use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.”
Into Function
"Into function is a function in which the set y has at least one element which is not associated with any element of set x."
Onto Function
"If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function."