Table of Contents

## What is a Function?

A function is a set of ordered pairs (x, y) where each element in the set corresponds to a unique output. The function assigns a unique output to every input.

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) = x^{2}. 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) = x^{2} + 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.

## Different Types of Representation of functions in Maths

There are different ways to represent functions in maths. One way is to use a graph to show the relationship between the input and output values. The graph will show the y-axis as the output value and the x-axis as the input value. Another way to represent functions is with an equation. The equation will show the relationship between the input and output values, and will also include the equation’s variables.

## Representation of Functions

A function can be represented in a variety of ways, including as a graph, table, or equation. In a graph, the function is represented by a curve that typically rises and falls as it moves across the coordinate plane. In a table, the function is represented by a list of values that the function takes on. In an equation, the function is represented by a formula that assigns a unique value to each input. 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

The algebraic representation of a function is a mathematical way of describing the function using variables and equations. This representation can be used to find the equation of a graph, or to find the inverse of a function.

## What is the Function Table?

The function table is a table that shows the input, output, and domain and range of a function.

## Graphical Representation of Function

A graphical representation of a function is a graph that shows the relationship between the input and output of the function. The input is typically graphed on the horizontal axis, and the output is graphed on the vertical axis.