Functions and Equations

An equation is a statement where two expressions are equal. Here left and right side will be equal. 

Suppose x + 3 = 10. For a particular value x, the equation will be satisfied. If x=7 then 7+3=10. The left and right side are equal.

Function is a bit different. It is a relationship between two variables. Function is written as f(x)=x+3. It takes a set of value as input and return a particular output. The input variable f(x) is called Independent variable because it takes input as f(0),f(1),f(2) etc. and returns corresponding output as 3,4,5 etc. x + 3 is dependent on f(x) that's why x+3 is called as Dependent variable.

In equation, we need a particular value of variable to make it equal where function takes a set of  permissible input and returns regarding output.

What is Function in Mathematics?

A function in mathematics is just like relation between input and output. So a function takes input and returns an output. It is denoted as f.  Most of the time, you see it in below form.

f(x) = x² + 1 

For a given value of x, you will get the result of  x² + 1.

Value of x	Output
0 1 2 3 4	1 2 5 10 17

We see that for a particular value of variable x, we get a corresponding output. This phenomena is called function in mathematics.

We shall denote function of x as f(x), F(x), φ(x) etc.

The number x that we use for the input of the function is called the 'Argument' of the function. It may seems to us that we can pick any number as argument  and for this reason we can call it 'Independent Variable' and the output of the function, e.g. f(x), f(3), etc. depends upon the argument, can be called the 'Dependent  variable'.
We can draw a picture of a function on graph by taking argument-value pairs of the function and describing each by a point in the plane, with x coordinate given by the argument and y coordinate given by the value for that pair.