Equations vs Functions: Difference and Comparison

When a student is learning the subject of algebra, the difference between a function and an equation is always unclear. Equations and Functions are two different topics in the matter of algebra.

Key Takeaways

  1. An equation is a mathematical statement that equates two expressions, while a function is a mathematical rule that assigns a unique output for every input.
  2. An equation can have multiple solutions, while a function has only one output for every input.
  3. Equations are used to solve problems or find unknown values, while functions describe relationships between variables.

Equations vs. Functions

The 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 vs Functions

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 word.

Functions are a topic in algebra used by a person to solve problems using variables. When explaining what functions are in algebra, it seems to be a pretty broad topic to be understood.

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Comparison Table

Parameters of ComparisonEquationsFunctions
Solved byThe sums are solved by a person based on the value that they are equated within an equation.A person solves the sums based on values assigned to a function’s variables.
CharacteristicIt is a superset of a function.It is a subset of an equation.
GraphThere can be representation on graphs of an equation.There can sometimes be no representation of graphs of a function.
Number of variablesAn equation is capable of having more than one value for its variable.A function cannot have two values for its variable.
Points in graphIn 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 word.

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.

An equation, in short, means finding the value of a specific variable given in the problem. Following are some examples of the equation.

  1. 2a + 3a = 15; what are (a) values?
  2. 4a + 6a = 24; what are (a) values?
equations

What are Functions?

Functions are a topic in algebra used by a person to solve problems using variables. When explaining what functions are in algebra, it seems to be a pretty broad topic to be understood.

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.

A letter such as F, a, or g denotes the word function in any algebraic expression. Following are some examples where the problems are solved by using parts.

  1. F(x) = 3x + 5
  2. F(g) (x) = 6y+9
functions

Main Differences Between Equations and Functions

  1. An equation can have more than one value for its variable; conversely, a function cannot have two values for its variable.
  2. 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.
Difference Between Equations and Functions
References
  1. https://ui.adsabs.harvard.edu/abs/1964RuMaS..19R…1L/abstract
  2. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.51.5153
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