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Functions, image, Linear Function, Unit Function, Constant Function, One…
Functions
Types of Functions
In number theory, the unit function is a completely multiplicative function on the positive integers
It is called the unit function because it is the identity element for Dirichlet convolution.
It may be described as the "indicator function of 1" within the set of positive integers. It is also written as u(n) (not to be confused with μ(n), which generally denotes the Möbius function).
A constant function is a function which takes thesame value for f(x) no matter what x is. When we aretalking about a generic constant function, we usuallywrite f(x) = c, where c is some unspecified constant.
A linear function is a function that represents astraight line on the coordinate plane. For example, y= 3x - 2 represents a straight line on a coordinateplane and hence it represents a linear function.
If the horizontal line intersects the graph at morethan one point anywhere, then the function is notone-to-one.
If the horizontal line intersects the graph at onlyone point everywhere, then the function is one-to-one.
Into function is a type of function that establishesa binary relationship between two sets such thateach element of the first set (domain) is associatedwith exactly one element of the second set(codomain), and at least one element of thecodomain is not associated with any element in thedomain.
A and B are thetwo sets, if for every element of B, there is at leastone or more element matching with set A
Use of Functions in Daily Life
In vehicles; Movement up and down the passenger seat due to bumps in the road for vibration is expressed in function.
In stock market charts, money, currency, gold, oil, exchange values are shown and the function is used in every chart display.
There are so many real-life situations that can be defined, solved, and understood if they are related to functions. Functions can be graphed, thereby visualized, and other concepts and discoveries can be observed and made.
History of Functions
The term function was first used by Rene Descartes, a French philosopher, scientist, and mathematician, in 1637 to designate a power x n of a variable x. Gottfried Leibniz applied the term to various aspects of a curve in 1694. Peter Dirichlet, in 1829, did further work on functions.
Definition of a Function
Let there be a relation from set A to set B (A≠ ∅ and B≠ ∅).
If every element in A corresponds only one element in B, then the relation is called a function.
-Every element of A must be paired with one element in B
-An element of A cannot be paired with more than one element of B.
Finding the Value of Functions
Let f be defined on R. (f:R → R) Each element in the domain is mapped with three more than twice itself.
Linear Function
Unit Function
Constant Function
One-to-One Function
Into Function
Onto Functions
