At functions and the equations are very similar mathematical contents, but they have differences that often go unnoticed by students. Before listing the differences between these important expressions, we'll show you examples of functions and equations To compare.
Equation Examples
1) 2x + 4 = 0
2) 2x2 – 18 = 0
Function examples
1) y = 2x + 4
2) y = 2x2 – 18
From the examples above, you can see that: both functions as to equations have unknown numbers, that can be represented by the letter x; they are math operations and an equality. However, we can differentiate these concepts based on their properties and definitions. See below the basic definitions of functions and equations and get to know some of their properties:
Equation and Function Definition
One equation is an equality between the elements of two members, where those elements are the result of math operations between known and unknown numbers.
One occupation is math rule that lists each element of a set A to a single element of a set B. Looking at the examples, it can be said: for every number x that belongs to set A, there is a unique number y in set B. So x is called variableindependent and y dependent variable.
Therefore, the first differencein between at functions and the equations is in your definitions. While the equation is a more basic expression, the function is a rule that relates numbers from two sets.
Difference between unknown and variable
Unknown is the name by which x is called in a equation (or any other letter that represents a number). In equations, the central idea is that each unknown represents a number, which may (or may not) be discovered using the properties of the equations. For example, in the equation 2x – 6 = 0, the unknown x is equal to 3, because, replacing x by 3, we have:
2x - 6 = 0
2·3 – 6 = 0
6 – 6 = 0
Variable is the name by which x is called in functions (or any other letter that represents a number). In addition to the variable x, a function also has, by definition, a variable f(x) or y. The idea is that a variable has no fixed value, that is, the variable x can take any value inside the domain, and the variable y can take any value inside the counterdomain, depending on the law of formation of the function. Note the y = 2x function:
If x = 0, y = 2·0 = 0
If x = 1, y = 2·1 = 2
And so on.
Therefore, the difference in between unknown and variable is as follows: the variable can take infinite values within your domain/counterdomain, and the unknown is a fixed result that cannot assume other values.
Difference between the results found
From the difference previous between incognitos and variables, we realized that the results found in equations are different from results found in functions.
In the equations, the result searched for is the value of x (da unknown) that satisfies an equality. In this case, the number of results found will be equal to or less than the degree of equation, when it is possible to resolve it. Therefore, a quadratic equation will have, at most, two values of x that satisfy the equality that defines it.
In the functions, each value of a variable is linked to a value of another variable through the training law. So, the results found are usually numerical sets that can be geometrically represented by graphics.
Relationship between function and equation
In general, the functions depend on the equations to exist. This is because the formation laws that represent the functions are precisely composed of equations. So, we can say that functions are the next step to be taken, right after learning all the details about equations. All properties, plus the method used to resolve equations, are also used in the calculations that can be done in the functions.
