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.

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