Representation of Functions

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What is a Function?

A function may be a relation between two sets of variables such one variable depends on another variable. We can represent differing types of functions in several ways. Usually, functions are represented using formulas or graphs. We can represent the functions in four ways as given below:

  • Algebraically

  • Numerically (Table Representation)

  • Visually

  • Verbally (Graphical Representation)

Each representation has its own advantages and disadvantages. Let’s just look and try to understand.


Different Types of Representation of functions in Maths

An example of an easy function is f(x) = x2. In this function, the function f(x) takes the given value of “x” and squares it.

For instance, if x = 3, then f(3) = 9. A few more examples of functions are: f(x) = sin x, f(x) = x2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc.

There are several types of representation of functions in maths. Some important types are:

  • Injective function or One to at least one of the functions: When there is mapping for a variety for every domain between two sets.

  • Surjective functions or Onto function: Whenever there is more than one element is mapped from the domain to range.

  • Polynomial function: The function which consists of polynomials.

  • Inverse Functions: The function which inverts another function.

These were a few examples of functions. Point should be taken that there are many other functions like into function, algebraic functions, etc.


Representation of Functions

The function is the link between the two sets and it can be represented in different ways. Consider the above example of the printing machine. The function that shows the connection between the numbers of seconds (x) and therefore the numbers of lines printed (y). We are quite conversant in functions and now we'll find out how to represent them.


Algebraic Representation of Function

It is one among the standard representations of functions. In this, functions are explicitly represented using formulas. The functions are generally denoted by small letter alphabet letters. For e.g. let us take the cube function.


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The standard letter to represent function is f. However, it can be represented by any variable. To denote the function f algebraically i.e. using the formula, we write:

f : x → x3

where x is the variable denoting the input. It can be represented by any variable.

x3 is the formula of function

f is the name of the function

Even if it is one of the easiest ways of representing a function, it is not always easy to get the formula for the function. For such cases, we use different methods of representation.


In this method, we represent the connection within the sort of a table. For each value of x (input), there's one and just one value of y (output). The table representation of the problem:


Table Representation of Function

X (Second)

Y (Number of Lines)

1

100

2

130

4

160

6

190

8

220

10

250

12

280

14

310

15

325


What is the Function Table?

A function table is a table of ordered pairs that follow the relationship, or rule, of a function. To make a function table for the example, first let us figure out the rule that shows our function. We have that every fraction of each day worked gives us that fraction of \[$\] 200. Thus, if we work at some point , we get \[$\] 200, because 1 * 200 = 200. If we work for two days, we get \[$\] 400, because 2 * 200 = 400. If we have to work for 1.5 days, we get \[$\] 300 in amount, as 1.5 * 200 = 300. Are we seeing a pattern here?


To find the entire amount of cash made at this job, we multiply the amount of days we've worked by 200. Thus, our rule is that we take a worth of x (the number of days worked), and that we multiply it by 200 to urge y (the total amount of money made).


A function table is used to display the rules. In the first row for the function table, we put the values of x, and in the second row of the table, we put the corresponding values of y which is according to the function rule.


x = # days worked

1

2

3

3.5

5

7.25

8

y = total money made

200

400

600

700

1000

1450

1600


Graphical Representation of Function

Here, we'll draw a graph showing the connection between the 2 elements of two sets, say x and y such that x ∈ X and y ∈ Y. Putting up the satisfying points of x and y in their own axes. Drawing a line passing through these points will represent the function during a graphical way. Graphical representation of the above problem:


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FAQ (Frequently Asked Questions)

Question 1) What is the Representation of Function in Math?

Answer) Representation of functions are generally represented by a function rule where we express the variable , y, in terms of the known experimental variable , x. y =2.50⋅x. We can represent that function by putting it into a graph. The normal way to create a graph is by creating a table which contains different inputs and their corresponding outputs.

Question 2) What is a Representation of Function?

Answer) A function is a relation between two sets of variables such that one variable depends on another variable. We can represent differing types of functions in several ways. Usually, representation of functions are done using formulas or graphs.

Question 3) How can you Identify a Function?

Answer) Verify the graph to see if any of the vertical lines drawn will intersect the curve more than once. If there is such a line,then the graph doesn't show us the representation of function. If no vertical line can intersect the curve quite once, the graph does represent a function.

Question 4) What Does Representation Mean?

Answer) Representation aids us to arrange, record, and communicate mathematical ideas and it helps us to unravel problems. In addition, we will represent mathematical ideas externally and internally. With these mathematical representation objects, we will represent objects and actions to form it easier to know them.