Equations and functions they are contents of the Mathematics discipline generally studied, respectively, in the seventh and ninth years of elementary school. As they are complementary contents, functions need equations to exist, so their similarities are great. However, it is important to know how to differentiate the two concepts so that studies at this stage are done more clearly and so that high school does not become a greater challenge.
To do so, look at two examples of equations:
a) 4x + 2 = 23 - x
b) x2 + 23 = 0
Now compare these equations with the following two examples of functions:
a) f (x) = 3x – 21
b) f (x) = x2 + 23
both the functions as to equations have at least one unknown number, which, in the examples above, is represented by the letter x. Furthermore, both concepts depend on a relationship of equality, established by the symbol “=” and mathematical operations such as addition, subtraction and multiplication.
Likewise, their differences are also basic, and the first one is precisely the definition of occupation it's from equation.
Function and Equation Definition
One equation is an equality between algebraic expressions. When these expressions have only one unknown number, called unknown, it may be possible to find it by solving the equation. In this way, an equation has unknown numbers, known numbers, and an equality.
One occupation is a rule that relates each element of a numeric set to a single element of another numeric set. This rule is just an algebraic expression represented in a similar way to the equations. However, to show that there is a relationship between elements of two distinct sets, on the one hand, use f (x) or y and, on the other, use x.
So, the functions make use of equations as rules that relate elements between sets. Remember that, in functions, the unknown numbers x and f (x) are called variables, which are, respectively, independent and dependent, respectively.
Difference between unknown and variable
At incognitos are the unknown numbers of equations. When an equation is solved, the result sought is precisely the value of the unknown in question. Example: 4x – 8 = 0. Note the solution to this equation:
4x - 8 = 0
4x = 8
x = 8
4
x = 2
So, the equations have an exact and fixed number of possible outcomes for each unknown. First degree equations have only one result, and first degree equations high school present two results and so on.
In functions, the amount of results is variable and, therefore, the unknown number receives the same name. The results depend on the set in which the occupation has been set. Example: let's say that the function f (x) = 2x is defined on the set of real numbers. For every real number x, there is a real number f (x) related to x. Thus, for x = 2, we will have f (x) = 2·2 = 4. For x = 3, we will have f (x) = 2·3 = 6.
difference between results
In the functions, it is more important to know how the rule relates the elements of two sets than the elements themselves. So, if you can graph a function, you can also see its behavior and in a way, knowing how each of the elements of the first set relates to the elements of the second set.
The result of a equation, however, is just a number that can mean anything or nothing, depending on the context in which this equation was created. It is important to realize that when evaluating the behavior of a occupation at one point, that is, by replacing x with a number in a function, we will end up in a problem in which knowledge of equations will be used. Example: What is the value of x related to 16 in the function: f (x) = 2x + 8? To find this result, just replace f (x) = by 16 and solve the resulting equation.
f (x) = 2x + 8
16 = 2x + 8
16 - 2x = 8
– 2x = 8 – 16
– 2x = – 8
2x = 8
x = 8
2
x = 4
Therefore, functions and equations they are complementary knowledge. A function can be said to use an equation to relate elements between sets.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/diferencas-entre-funcao-equacao.htm