Introduction To Functions


Introduction to Functions in mathematics can be given by representation of relationship between a set of variables and constants. These are used to solve equations for unknown variables. A function possesses unique output or value for each and every input on it. Introduction to function in its simplest form can be given as: y = x. For any value of 'x' we insert in the function, same will be the value of 'y', so, here 'y' is said to be dependent on 'x'. Mostly complex functions involve mathematical operations being applied to 'x' to determine the final value of 'y'. For example, if we take y = x2 + 5x + 6. Here, first we need to simplify the function in 'x' using factorization method. Then for two possible values of 'x' we get two values of 'y'. In functions, values will change, but relationship between variables remains constant.

A much known form to represent a definition function is: f(x).

Mostly functions are written with f(x) in place of 'y'. For example, f(x) = 4x. In this notation, function of 'x' is equals to four times the value of 'x'. So, for any value of 'x' say 2, function of 'x', or f(x) is equals to 8.

Evaluating a function means solving a mathematical problem or equation involving a function. For this we need to provide an input. For each input given for variable 'x', there can be only one output for function.

For example, in function f(x) = 20x, inputs can be given as:




and corresponding values or outputs of functions that we get will be:

x=2, f(x) = 40,

x=3, f(x) = 60,

x=5, f(x) = 100,

Functions are of importance in various fields of maths, physics, science etc.

Topics Covered in Introduction To Functions

Interpreting Graphs

To interpret a graph means discussing the characteristics of an algebraic expression. Abstract equations, functions, expressions and concepts become more clearly visible when projected on an x / y coordinate plane, also known as a Cartesian coordinate system. Interpreting graphs means determining the 'x' and y- coordinates for an equation which becomes mor...Read More

Applications of Functions

Function can be defined as representation of variations in output by change in values of the inputs. In other words we can say that function shows the relationship between a set of inputs and outputs. Here it is confirm that each input belongs exactly to one output. In a function, input to a function is called argument and output is called as value. ...Read More

Math Topics