Function and Graph

This one of my favorite topic. And may be that the reason the first one in series of topics I had taken to share with you all !!!

Function  - for every x there is exactly one y. 

x ----->Operator --------> y

Here, x is the input. Function is like some operator, you can think of a machine and y as the output.

Now, 

x ----->Function --------> y

The values x can take is called DOMAIN

and the Y values can get is called RANGE.

Remember, for every x there is exactly one y, the first sentence of function definition.

Note that x and y are related to each other by this operator - Function.

Lets, take an example.

y = x^2 + 2

here, operator or function is x^2 + 2,

we can denote this function as f(x) = x^2 + 2

f(x) is called function of x, as it can take independent values to give values for f(x).

All the values x can take is its domain and all the values f(x) will get will range.

lets give some values to x,

x = -1  f(-1) = 1+2 = 3

x=0      f(0) = 0+2 = 2

x=1     f(1) = 1+2 = 3

x= 2    f(2) = 4+2 = 6

Also, note f(x) has unique value for each x. 



We took few values as input for the operator f(x) but x can take other values which can be

from   - infinity to + infinity.

Range will be as you can see from the graph 2 to + infinity.