When a student is learning the subject of algebra, the difference between function and an equation is always unclear. Equations and Functions are two different topics of the subject of algebra. There often arises a blur between a function and an equation as both use variables to solve their equation. Although they both use variables, they do have their differences.
Equations vs Functions
The main difference between an equation and a function is that in an equation, a person solving an equation can have either one or two values based on the number of variables they have put into use for solving that equation, and on the other hand, is a function a person will always have solutions based on the Input they have chosen to solve their question.
Equations are a topic used in algebra to solve problems through variables. These equations act as a statement to denote the equality of a variable on both the left and right sides of a statement. When a person wants to show equality between two variables, the sign = is used to denote equality.
Functions are a topic in algebra used by a person to solve problems using variables. When it comes to explaining what functions are in algebra, it seems to be a pretty wide topic to be understood. A function is said to be formed when a value of one variable of a set is paired with a value of another variable from another set.
Comparison Table Between Equations and Functions
| Parameters of Comparison | Equations | Functions |
| Solved by | The sums are solved by a person based on the value that they are equated with in an equation. | The sums are solved by a person on the basis of values that are assigned for the variables in a function. |
| Characteristic | It is a superset of a function. | It is a subset of an equation. |
| Graph | There can be representation on graphs of an equation. | There can sometimes be no representation of graphs of a function. |
| Number of variable | An equation is capable of having more than one value for its variable. | A function cannot have two values for its variable. |
| Points in graph | In a vertical test for equations in a graph, a person can intersect at one or two points at a line. | A person can intersect at multiple points in a graph at a line in a vertical test for functions. |
What are Equations?
Equations are a topic used in algebra to solve problems through variables. These equations act as a statement to denote the equality of a variable on both the left and right sides of a statement. When a person wants to show equality between two variables, the sign = is used to denote equality.
In a function, the right and the left side are always told to be equal. They are always said to have an inverse relationship being unitary by nature when solved. An equation always contains more than one variable. They are most commonly used for Algebraic calculations to make it easier to find the solutions. There are also some types of equations such as Quadratic equations, linear equations, etc.
An equation, in short, means finding the value of a specific variable given in the problem. Following are some examples of the equation.
- 2a + 3a = 15, what are the values of (a)?
- 4a + 6a = 24, what are the values of (a)?
What are Functions?
Functions are a topic in algebra used by a person to solve problems using variables. When it comes to explaining what functions are in algebra, it seems to be a pretty wide topic to be understood. A function is said to be formed when a value of one variable of a set is paired with a value of another variable from another set.
In most schools, a function is always taught to a child as a rule which is taken as each set of a member x and mapped to the same value of y on the page. When a person wants to denote a Function between two variables, he must express it as F → function → y.
A letter such as F, a, or g is used to denote the word function in any kind of algebraic expression. Following are some examples where the problems are solved by using functions.
- F(x) = 3x + 5
- F(g) (x) = 6y+9
Main Differences Between Equations and Functions
- In an equation, the sums are solved based on the value that they are equated with, and on the other hand, it is a function. The sums are solved on the basis of values that are assigned for the variables.
- Equations are supersets of functions, and on the other hand, functions are subsets of equations.
- All equations can be represented on a graph, and on the other hand, not all functions can be represented on a graph.
- An equation is capable of having more than one value for its variable, and on the other hand, a function cannot have two values for its variable.
- In a vertical test for equations in a graph, a line can intersect at one or two points, and on the other hand, in a vertical test for functions, a line can intersect at multiple points in a graph.
Conclusion
Equations and Function are both statements in mathematics used For solving problems by a person. When a student is learning the subject of algebra, the difference between both a function and an equation is always unclear. Equations and Functions are two different topics of the subject of algebra.
There often arises a blur between a function and an equation as both use variables to solve their equation. Although they both use variables, they do have their differences. One should know the differences between them to be able to solve problems related to those concepts. They both are very essential and most commonly used for solving algebraic sums.
References
- https://ui.adsabs.harvard.edu/abs/1964RuMaS..19R…1L/abstract
- https://journals.aps.org/prd/abstract/10.1103/PhysRevD.51.5153