Representation of a Function

A function is a relationship between two sets of variables in which one variable is influenced by the other. Different sorts of functions can be represented in various ways. Formulas or graphs are commonly used to represent functions. A function can be represented in one of four ways, as shown below:

• Algebraically

• Numerically

• Visually

• Verbally

Graphical Representation : 

We’ll make a graph that depicts the relationship between two elements of two sets, say x and y, such that x∊X and y∊Y. The satisfied points of x and y in the corresponding axes are plotted. A graphical representation of the function can be represented by drawing a straight line through these places. The following is a graphic illustration of the problem:

Analytical Representation :

Consider an example of a printing machine. The relationship between the number of seconds (x) and the number of lines written is represented by this function (y).

The function will be represented below by a simple algebraic equation: f(x) = y =50 + 7(x). The values of y = f(x)) alter in response to varied x values. What if someone wanted to know how many lines the machine printed in 25 seconds? Simple math: y = 50 + 7(25) = 225 words printed. 

Tabular Representation :

A table is used to represent the relationship. There is only one value of y (output) for each value of x (input).

Below is the representation :

Ways of Representing :

In mathematics, there are various different ways to represent functions. The following are some examples of important types:

• One of the functions is an injective function, or one of the functions is an injective function: When there is a mapping between two sets for a range of domains.

• When more than one element is transferred from the domain to the range, subjective functions or Onto functions are used.

• A polynomial function is one that is made up of polynomials.

• The function that inverts another function is known as an inverse function. 

Examples :

Example 1. 

Let the function be f(x) = y = 1-x

Example 2 :

Let the function be f(x) = y = x2

Example 3 :

Let the function by f(x) = y = 3x-2 

Conclusion :

Different variables are frequently related in both real life and algebra. A relation is a term used to describe how variables interact when they change at the same time. A function is a relationship in which one variable dictates the exact value of another variable. Graphs, tables, and sets of ordered pairs can all be used to recognise, characterize, and investigate functions.