# 5 Representations of Relations and Functions

## What to Know?

This article would help us learn the basics on relation and its definition, function and its definition, domain and range of a relation or function, representations of relations and function, and its relationship to each other.

## Relation Vs. Function

### Relation

Consider a set of ordered pairs S: {(1,3),(2,6),(3,9)}; in this set of ordered pairs, each ordered pair *(x,y)* has elements *x* and *y*. Elements corresponding to *x* are called **domain** of the given ordered pairs while elements corresponding to *y* are called the **range** of the given ordered pairs. If a relation is any set of ordered pairs, then it means that a relation is a rule that relates values from a set of values of domains to the set of values from range. The elements of the domain can be imagined as input to a machine that applies a rule to these given inputs to generate on or more output. If a relation is a correspondence, then it has three types–one-to-one correspondence, many-to-one correspondence, and one-to-many correspondence.

**Function**

It is defined as a special type of relation in which every element in the domain is mapped to exactly one element in the range. If we considered a set of ordered pairs as a function, then there should be no two distinct ordered pairs having equal abscissas or having similar x element.

## 5 Representations of Relations and Functions

### 1. Ordered Pairs

A set of ordered pairs consists ordered pair or ordered pairs. Each ordered pair has elements *x* and *y. *An ordered pair is written in the form *(x,y)*. All values possible for *x* in a given rule is called the domain while all possible values for *y* in a given rule is called range.

Examples: a. (1,2) b. (2,4) c. (3,6) *Ordered Pairs*

d. S: {(1,2), (2,4),(3,6)} *Set of Ordered Pairs*

### 2. Mapping Diagram

A mapping diagram is visual representation of a relation or function. It shows the correspondence of a relation or function. A correspondence can be one-to-one, one-to-many, many-to-one. Among these three correspondence, one-to-many is not a function, while the other two are functions. *(See the photos below to visualize these correspondence as mapping diagrams.)*

### 3. Table of Values

A relation or function can be represented using a table of values. A table of values can be horizontal table or vertical table. It presents the elements of domain and range in tabular way. *(See the photo below.)*

### 4. Graph

A relation or function can also be represented through a graph. A graph is the set of points in Cartesian Plane that represents the given rule or equation of a relation or function. *(See the photo below.)*

*The Vertical Line Test*

To determine whether a given graph illustrates a function or not, vertical line test is used. If every vertical line intersects the graph no more than once, the graph represents a function.

### 5. Rule or Equation

Rule or equation describes the relation or function; usually *y* is written in terms *x*, where *y* is the dependent variable and *x* is the independent variable. To emphasize or show that *y* is a function, *y* is usually written as *f(x)*. This rule or equation is also useful in determining the values that are possible elements of domain; as well as possible values as elements in the range. It is used to identify if a certain value for x is an element of the domain or not.

## Try your Understanding!

For each question, choose the best answer. The answer key is below.

**It is a special type of relation in which every element in the domain is mapped to exactly one element in the range.**- Function
- Relation
- Correspondence
- Range

**It describes a relation or function; usually y is written in terms x.**- Graph
- Mapping Diagram
- Equation/Rule
- Ordered Pair

**It is used to determine whether a given graph illustrates a function or not.**- Equation
- Vertical Test
- Horizontal Lines Test
- Vertical Line Test

**It is a visual representation that shows the correspondence of a relation or function.**- Pie Graph
- Correspondence
- Mapping Diagram
- Table of Values

**Which of the following does NOT represent a function?**- One-to-many correspondence
- One-to-one correspondence
- Many-to-one correspondence
- None of the above

### Answer Key

- Function
- Equation/Rule
- Vertical Line Test
- Mapping Diagram
- One-to-many correspondence

## Your Reflection!

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use? You can leave your answer in the comment section.

**© 2020 Ryan Bernido Network**

## Comments

**courage** on October 22, 2020:

from the equation to table of values then the graph sends the message loud and clear

**Criselle Morano** on October 01, 2020:

Among the five representations, using a graph for me is the most convenient. It easily represents the function or relation through of points. By just looking to the graph it is not too complicated to determine relations or functions compared to other representations.

**Sheena Antoneth M. Mendones** on October 01, 2020:

For me, the most convenient representation to use is the graph because the function will be easily determined through the use of vertical line test.

**Ericka Kaye Gison** on October 01, 2020:

In my opinion, out of the 5 representations of relations or functions-ordered pairs, graph is more convenient to use. You can just look at the graph and use the vertical line test to know whether it is a relation or a function.

**Majah Angelika Cagampang** on October 01, 2020:

From the given representations of functions and relations, I find the table of values convenient. The reason is because for me, it is a good combination of being efficient to prepare while also being easy to check whether there are repeating values.

**Hazel Ann Naz Villacorta** on October 01, 2020:

I think, ordered pairs is more convenient to use because you can easily identify if it's a relation or a function just by looking at the domain.

**Reina Mae Naz Mostar** on October 01, 2020:

Among the five representations of relations or functions, the most convenient for me to use is the Table of Values since values of both the domain and range are presented in a tabular form which makes it more organized compared to the other representations.

**Ellyzabelle Louise Y. Donor** on October 01, 2020:

In my opinion, the most convenient representation of relations or functions among the five is the table of values because it clearly shows the list of domains, which could be of help to identify functions and relations much easier.

**Crizielle Reniva** on October 01, 2020:

Among the five representations, I personally think that the mapping diagram is the most convenient one because it easily shows how the elements are paired.

**Hannah Jade M. Adille** on October 01, 2020:

For me, the mapping diagram is the most convenient to use because you can easily determine if a value of x was paired more than once through the guide of arrows that will help you in recognizing if the set of ordered pairs is a function or a relation.

**Clint Xander Nieva** on October 01, 2020:

For me, the most convenient one to use is the vertical line test. Because I can easily tell if it is a function or relation even just by looking at it

**Kristine F. Daroy** on October 01, 2020:

Among the five representations of relations or functions the more convenient to use for me is mapping diagram because it is easy for me to visualize the sets. Through arrows i can already see if the domain corresponds to range more than once and eventually tell if the sets is function or not. I find this more useful compare to others.

**Mark Joe Saturnino** on October 01, 2020:

For me, the most convenient among the five representation of function and relation is the table of values because it clearly illustrate what is the repeating domain that corresponds to a range,thus it can shows if the ordered pairs is a function or a relation.

**Kyla Victoria** on October 01, 2020:

Among the five representations of function and relation, the most convenient to use for me is the ordered pair. You can easily determine whether it is a function or not by just looking at the domain or the x values.

**Gloria Bicaldo** on October 01, 2020:

Among the five representations of relations and function, for me, the most convenient representation to use is the mapping diagram because, with the arrows, you can easily identify if it is a function or relation.

**Rosa Maria Palencia** on October 01, 2020:

It think it is more convenient to use the ordered pair representation because it doesn't take up too much space.

**Hector C. Vargas** on October 01, 2020:

Graph is convenient to use because I can easily determine wether it is a function or by just drawing a vertical line.

**Carmela Llaguno** on October 01, 2020:

For me, the most convenient to use is mapping diagram it shows the corresponding by a two diagram and a arrow where it can see easily if it is relation or function.

**Sean Elijah Zano** on October 01, 2020:

The most convenient one to use for me is the graph. This is because I can easily tell if it is a function or relation just by looking at it.

**Agao, Cheene Jane** on October 01, 2020:

Among the five representations of relations or functions, I think the most convenient to use is the mapping diagram since the corresponce either it is one-to-one or many-to-one or one-to-many can easily be seen. It clearly shows the relationship between the x and y-values.

**Gillian Gobangco** on October 01, 2020:

The most convenient for me is the ordered pairs, since it is the easiest, you can quickly determine the domain and range/ x and y, and if the given is a function or not, just on the first look.

**Hazel Ann N. Villacorta** on October 01, 2020:

I think, ordered pairs is more convenient to use because you can easily identify if it's a relation or a function.

**Earl James D. Garcia** on October 01, 2020:

Personally, I find the table of values to be of most convenience among the five representations. At a glance, I can easily determine which is which.

**Hanzel N. Vidar** on October 01, 2020:

For me, the more convenient representation of relation or function to be use is mapping diagram because it clearly shows the pairing between two elements and the arrows help a lot in order to easily understand it.

**Ryszard Roy B. Beldia** on October 01, 2020:

Personally, the most convenient one to use is the mapping diagram. At first glance, it is looks a lot less intimidating compared to a graph. It's also easier to see the relations of the values by using arrows.

**Kriztyn Miden L. Rosanes** on October 01, 2020:

Among the five presentation, the most convenient to use for me is the mapping diagram for i can easily represent the relation of the elements in x and y by drawing arrows and it can also be easily understood or interpreted.

**Janus Martin B. Villar** on October 01, 2020:

From the five representations, I think the most convenient for me personally is the use of Graph. Because I can easily determine if it's a function or relation by the visual presentation of a graph, while some presentation I find it somewhat vague.

**Marco F. Navera** on October 01, 2020:

Among the five representations of relations or functions, the most convenient one to use for me is the mapping diagram because it makes use of arrows to show correspondence. By just merely looking at the number of arrows from an element of the first circle, we can already tell if one domain corresponds to one range or if it corresponds to two or more range values, which is the primary indicator whether the relationship is a function or a relation.

**Hannah Mae A. Paguio** on October 01, 2020:

i think among the five representations of relations or function, the most convenient to use is the mapping diagram since there is an arrow to show whether the domain is connected to one range only or not which makes its not confusing and time consuming in terms of determining whether it is a function or a relation

**MORALES, Ammie Faye Sistina** on October 01, 2020:

Among the 5 representations, the most convenient for me is the Table of Values. The sets of ordered pairs are already tabulated where I can easily determine those with the same domains. Unlike the mapping diagram, I may be confused of the arrows.

**Sean Carlo Pradil** on October 01, 2020:

Among the 5 representations of relatiions or functions the most convenient for me is is the mapping diagram for it helps me visualize and clearly understand and choose what is relation and what is not

**Krish Micah Jahziel R. Jasareno** on October 01, 2020:

For me, ordered pairs is more convenient to use than the other representation of relation or functions because you're just going to look at the first elements or the domains of each pairs. You can determine if it's a relation if the domain is repeated in the domain of other pairs and function if there is only one domain for each pair.

**Jianne V. Garcia** on October 01, 2020:

For me the most convenient among the five representation is the ordered pairs because at one glance you can already identify which is a function and a relation.

**Regine M. Adivino** on October 01, 2020:

For me, in representing the function or relation, the most convenient way to use is the table of values. With this, I can easily identify which is a function or relation just by looking at the column or row of the domain.

**Angela Naris** on October 01, 2020:

Among the five representations of relations and functions, for me, the graph is the most convenient. It is because it's easy for me to identify if it is a relation or a function aside from the other representations which make me a little confused sometimes.

**Ma. Sophia Ajero** on October 01, 2020:

In my opinion, the mapping diagram is the most convenient use among the five representation of functions and relations because it clearly represents the relationship between the domain and range values

**Jonna Mae D. Yanson** on October 01, 2020:

For me among the five representations, the most convenient to use is the mapping diagram. It is because I can have the visual representation of the column for domain and range. Also, I can easily recognize whether it's a function or relation with the help of the one-to-one correspondence, many-to-one correspondence and the one-to-many correspondence.

**Bea Nicole Mahinay** on October 01, 2020:

Among the 5 representations of relations or functions, the most convenient is the mapping diagram because it clearly shows the difference between relation and function when it comes to how the domain and the range correspond to each other.

**Kaila Joy A. Abainza** on October 01, 2020:

For me, mapping diagram is more convenient to use than other representation of relations or function because I can easily visualize the relationship of the domain and range and identify whether it is a function or not.

**Angelica B. Panique** on October 01, 2020:

For me the most convenient to use in representation of relation or function is the ordered pairs. Determing if it is a relation or function is much easier when you use ordered pairs as long as you are a keen observer. It is also not time consuming unlike tbe other four.

**Ma. Christine S. Moreno** on October 01, 2020:

The most convenient to use is the Mapping Diagram because it clearly shows the relationship of values using arrows.

**Yeojie Mapula** on September 30, 2020:

among the five presentation, the most convenient to use for me is the mapping diagram because it clearly represent the column domain and range. also it is easy to know or determine if it is function or not.

**Li Shien E. Loria** on September 30, 2020:

As for me talking about “easy”, it is more convenient to use ordered pairs as a representation of relations and function. Given an ordered pair of Domain and Range (x, y) it is easy to identify which of the sets are functions and relations. But in relation to real life situations, I would likely choose to apply rule or equation. It is more convenient to apply in solving and identifying relations and functions. It uses equations that solves a certain problem that can be identified as a function or relation. The equation or rule can be used in solving different problems in our daily activities and daily problems that is connected in Mathematics and numbers. And for me, that is more convenient.

**Patrick Pagal** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use?

Among the five representations of relations or functions. I think table of values because I can indentify easily which is the relation or functions.

**Julianne Bianca Lita** on September 30, 2020:

The table of values are the easiest for me to use because it is easy to define which of them is the relationship or function by it's domain and range.

**Paul Ago** on September 30, 2020:

For me, among the five representations of relations and functions the table of values is the most convenient to use. In the table of values, I can easily determine if there is a repeated value; if the value repeats in the x values you can determine that it is not a function and if it didn't, it is a function.

**Rogyn Loquinarion** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use?

For me the most convenient to use is the graph , beacause in graph we can easily identify which is the function or not by using the vertical line test.

**Brian Angelo Dela Cruz** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use?

For me the most convenient is using the graph diagram.It easy for to identify which is the function or not just using the vertical line test.

**Clynt Justine O. Erasmo** on September 30, 2020:

For me, among the five representations of relations and functions the table of values is the most convenient to use. In the table of values, I can easily determine if there is a repeated value; if the value repeats in the x values you can determine that it is not a function and if it didn't, it is a function.

**Phoebe Maravilla** on September 30, 2020:

Among the five representations of relations and functions, I prefer using the table of values because I can easily understand and identify which of it is a function or not. And also I can easily determine if some values are repeated or not.

**Angeline Bo** on September 30, 2020:

For me the most convenient to use is the table of values because it is easy to identify which of them is the relation or function by its domain and range.

**Una L. Llacer** on September 30, 2020:

Among the five representations. For me the most convenient to use is the mapping diagram because I can easily determine if it's a function or not by just looking at the arrows.

**Carla Flor Losiñada** on September 30, 2020:

The table of values is more convenient to use because you can easily identify the domain and range. Aside from that I understand the lesson clearly when using the table of values. It can also save time.

**Vincent Gerard Balgemino** on September 30, 2020:

Among the 5 representations of function and relations, the most convenient representations of relation and functions are graph and Equation or rule. Because in Graph you can easily Identify the answer in the given problem using Vertical line test and Equation is also convenient because you only need to determine values that are elements of domain as well as the values of elements in the range.

**Marylourds Bernadette O. Co** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, the most convenient to use for me is the table of values because I can easily determine if it is function or not

**Jamie Rose Manalo** on September 30, 2020:

For me it is the mapping diagram because i can easily identity which is which and what is what.

**Key M. Suarez** on September 30, 2020:

Among the five representations of relations and functions, the table of values are more convenient to use cause it's easily showcase the x-values and the y-values. Also, you can also foresee the repeated value of domain and you can now simply identify if it is function or relation.

**Ivy Mae Aranel** on September 30, 2020:

Among all the five representations of relations or functions, it is the table of values that is more convenient to use because for me it can easily indentify.

**Trisha Mae Tabuzo** on September 30, 2020:

For me, the more convenient to use is mapping diagram because it is easy to determine if each of the values are repeated and identify if it is relation or function.

**Janine Vergara** on September 30, 2020:

Among the five representations of relations or functions I prefer to use the table of values. In the table of values even just a glimpse or sight you can identify which of them is a relation or function. It can be also in a horizontal or vertical table so it is more convenient for me.

**juliusecom.gandol@bicol-u.edu.ph** on September 30, 2020:

For me the Mapping diagram because I can easily identify with one is relation or function by the use of vertical line test.

**Mika Joy M. Lunas** on September 30, 2020:

Among the five representations of relations or functions the more convenient for me is the graph, because i can easily determine if its a function or not just by using the vertical line test.

**Ghienica D. Lucañas** on September 30, 2020:

For me among the 5 representations of relations it is more convenient to use the graph by using the vertical line test.

such as if any vertical line intersects the graph more than once, then the graph does not represent a function. And if it intersects once it is a function.

**Janine A. De la Rama** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use? For me the convenient to use is tha Mapping Diagram because it is easy to identify or determine if it's a function or relation.

**Jazreel Mae P. Villacera** on September 30, 2020:

Among the five representations of functions or relations. For me, the more convenient to use is the graph. Why graph? Because using the vertical line test you will easily recognize which is the function and relation. When it is function there is only 1 point at a time when you use vertical line. When it is not a function it contains 2 points that will intersect to the vertical line.

**Christine B. Lucila** on September 30, 2020:

For me, among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, the most convenient to use is the table of values because for I can easily identify and understand if it is function or not.

**Steve Dolz** on September 30, 2020:

For me among all the Five Representation of Relations or Function what I think is convenient to use is the Table of Value because it is easy to analyze while having skeptical and oraganization.

**Monica Jean Arango** on September 30, 2020:

For me the most convenient to use among the five representation of relations or functions is the table of values since it is easy to look if there is repeated value in the domain that can help me easily determine if the set of values is a function or a relation.

**Kiarra Queen Bragais** on September 30, 2020:

For me, graph is more convenient because by just using the vertical line test, I can easily find the answer

**Keith Renee Rayel** on September 30, 2020:

For me table of values is more convenient to use because you can easily identify which is a relation or function by its domain and range.

**Heather Rose G. Odda** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use? The mapping diagram is much more easier to use for me, because it helps me easily differentiate if it is a function or not.

**Jusfere Ractis** on September 30, 2020:

For me the most convenient for me to use is the graph, its because for me its easy to determine if a vertical line intersected more than once and no more than once.

**Nicole Hernandez** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, which do you think is more convenient to use? For me, the most convenient to use to identify if its function or Relation it is the Table of Values where it is easier to look the domain and the range if there is a repetition happened.

**Mary Ann Bataller** on September 30, 2020:

For me, among the five representations of relations or functions, the table of values is the most convenient to use. It can be easily understand by just looking at the table with the corresponding letter x for the domain and y for the range. It can also be presented either vertically or horizontally making it more convenient.

**Joan Mae Bogñalbal** on September 30, 2020:

For me the most convenient is using the graph diagram.I can easily identify which is the function or not just using the vertical line test.

**Adelene Josee B. Bañares** on September 30, 2020:

Among the five representation of relations and functions, the more convenient to use is the table of value. Because I can easily distinguish whether it is a function or relations

**John Edward G. Bobier** on September 30, 2020:

For me among the five representation of relations or functions, equation or rule for me is the most convenient to use, for i can easily to know and determine if it is relation or function

**Krisha Agnes Lunas Tanio** on September 30, 2020:

Among the five representations of relations or functions which is the ordered pairs, mapping diagram, table of values, graph, and equation or rule, for me the more convenient to use is the mapping diagram. It is easy to analyze the functions and relation when it is visualize. It is not hard to point out the relations and function when it comes to mapping diagram. That's the reason why I think Mapping Diagram is more convenient than the other respresentation

**Antonio Miguel Ajero** on September 30, 2020:

Among the five representations of relations or functions, the more convinient for me to use is the graph, because I can easily detect if it is a function or domain by using the vertical line test

**Joan Mae Bogñalbal** on September 30, 2020:

100%

**Mary Ann Bataller** on September 30, 2020:

For me, among the five representations of relations or functions, the table of values is the most convenient to use.

**Eunice Bernadette Barrid** on September 30, 2020:

Among the five representations of relations or functions–ordered pairs, mapping diagram, table of values, graph, and equation or rule, for me it is more convenient to use mapping diagram, for I can easily understand and determine if it is a function or not.