Difference between relationships and functions
The mathematical relationship is the link that exists between the elements of a subset with respect to the product of two sets. A function involves the mathematical operation to determine the value of a dependent variable based on the value of an independent variable. Every function is a relation but not every relation is a function.
| Relationship | Function | |
|---|---|---|
| Definition | Subset of ordered pairs that correspond to the Cartesian product of two sets. | Mathematical operation to be performed with the variable x to get the variable Y. |
| Notation | x R Y; x it is related to Y. | Y=ƒ(x); Y is a function of x. |
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What is a mathematical relationship?
It is called the binary relation of a set A in a set B or the relation between elements of A and B to every subset C of the Cartesian product A x B.
That is, if set A is made up of elements 1, 2 and 3, and set B is made up of elements 4 and 5, the Cartesian product of A x B will be the ordered pairs:
A x B = {(1,4), (2,4), (3, 4), (1,5), (2,5), (3,5)}.
The subset C = {(2,4), (3,5)} will be a relation of A and B since it is composed of the ordered pairs (2,4) and (3, 5), the result of the Cartesian product of A x B.
Relationship concept
"Let A and B be any two non-empty sets, let A x B be the product set of both, that is: A x B is formed by the ordered pairs (x, y) such that x is the element of A and Y it is from B. If any subset C is defined in A x B, a binary relation in A and B is automatically determined as follows:
x R Y if and only if (x, y) ∈ C
(the notation x R Y Means "x it's related to Y").
We will call set A starting set and we will call set B arrival set.
The relationship domain are the elements that make up the starting set, while the ratio range are the elements of the arrival set.
Example of mathematical relationships
Set TO from x elements of men in a population and B is the set of Y elements of women from the same population. A relationship is established when "x is married to Y".
What is a mathematical function?
When we talk about a mathematical function of a set A in a set B we refer to a rule or mechanism that relates the elements of set A with an element of set B.
Function concept
"Sean x Y Y two real variables, it is then said that y is a function of x yes to each value I take x corresponds to a value of Y."
The independent variable is x while Y is the dependent variable or function:
y = ƒ (x)
The set in which the x it is called domain of the function (original) and the variation of Yfunction range (picture).
The set of pairs (x, Y) such that Y=ƒ(x) is called function graph; if they are represented in Cartesian axes, a family of points is obtained called function graph.
Function examples
In mathematics we get many examples of functions. Here are examples of flagship functions.
Constant function
A function is called constant if the element of set B that corresponds to set A is the same. In this case, all values of x correspond to the same value of y. Thus, the domain is the real numbers while the range is a constant value.
Identity function
Let's suppose x is a variable and that Y takes the same value as x. We then have an identity function y = x, where the pairsx, y) on the graph are (1,1), (2,2), (3,3) and so on.
Polynomial function
A polynomial function fulfills the form y = anxn+ an-1+ xn-1+... + a2x2+ a1x + a0. The graph above shows the function ƒ (x) = x2+ x-2.
Now suppose that the dependent variable Y equals the independent variable x raised to the cube. We have the function y = x3, whose graph is shown below:
